# Download Mathematical Techniques of Fractional Order Systems Ebook PDF

**Mathematical Techniques of Fractional Order Systems**

A Book

#### by **Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan**

- Publisher : Elsevier
- Release : 2018-06-11
- Pages : 700
- ISBN : 012813593X
- Language : En, Es, Fr & De

Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from different perspectives in design, analysis and realizations, nonlinear fractional-order circuits and systems, the fractional-order memristive circuits and systems in design, analysis, emulators, simulation and experimental results. It is primarily meant for researchers from academia and industry, and for those working in areas such as control engineering, electrical engineering, computer science and information technology. This book is ideal for researchers working in the area of both continuous-time and discrete-time dynamics and chaotic systems. Discusses multidisciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results Includes circuits and systems based on new nonlinear elements Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers Closes the gap between theoretical approaches and real-world applications Provides MATLAB® and Simulink code for many applications in the book

**Fractional Order Systems**

An Overview of Mathematics, Design, and Applications for Engineers

#### by **Ahmed G. Radwan,Farooq Ahmad Khanday,Lobna A. Said**

- Publisher : Academic Press
- Release : 2021-10-13
- Pages : 612
- ISBN : 0128243341
- Language : En, Es, Fr & De

Fractional Order Systems: An Overview of Mathematics, Design, and Applications for Engineers introduces applications from a design perspective, helping readers plan and design their own applications. The book includes the different techniques employed to design fractional-order systems/devices comprehensively and straightforwardly. Furthermore, mathematics is available in the literature on how to solve fractional-order calculus for system applications. This book introduces the mathematics that has been employed explicitly for fractional-order systems. It will prove an excellent material for students and scholars who want to quickly understand the field of fractional-order systems and contribute to its different domains and applications. Fractional-order systems are believed to play an essential role in our day-to-day activities. Therefore, several researchers around the globe endeavor to work in the different domains of fractional-order systems. The efforts include developing the mathematics to solve fractional-order calculus/systems and to achieve the feasible designs for various applications of fractional-order systems. Presents a simple and comprehensive understanding of the field of fractional-order systems Offers practical knowledge on the design of fractional-order systems for different applications Exposes users to possible new applications for fractional-order systems

**Fractional Dynamics and Control**

A Book

#### by **Dumitru Baleanu,José António Tenreiro Machado,Albert C. J. Luo**

- Publisher : Springer Science & Business Media
- Release : 2011-11-19
- Pages : 310
- ISBN : 9781461404576
- Language : En, Es, Fr & De

Fractional Dynamics and Control provides a comprehensive overview of recent advances in the areas of nonlinear dynamics, vibration and control with analytical, numerical, and experimental results. This book provides an overview of recent discoveries in fractional control, delves into fractional variational principles and differential equations, and applies advanced techniques in fractional calculus to solving complicated mathematical and physical problems.Finally, this book also discusses the role that fractional order modeling can play in complex systems for engineering and science.

**Fractional Order Systems**

Optimization, Control, Circuit Realizations and Applications

#### by **Ahmad Taher Azar,Ahmed G. Radwan,Sundarapandian Vaidyanathan**

- Publisher : Academic Press
- Release : 2018-08-16
- Pages : 741
- ISBN : 0128163089
- Language : En, Es, Fr & De

Fractional Order Systems: Optimization, Control, Circuit Realizations and Applications consists of 21 contributed chapters by subject experts. Chapters offer practical solutions and novel methods for recent research problems in the multidisciplinary applications of fractional order systems, such as FPGA, circuits, memristors, control algorithms, photovoltaic systems, robot manipulators, oscillators, etc. This book is ideal for researchers working in the modeling and applications of both continuous-time and discrete-time dynamics and chaotic systems. Researchers from academia and industry who are working in research areas such as control engineering, electrical engineering, mechanical engineering, computer science, and information technology will find the book most informative. Discusses multi-disciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results Includes new circuits and systems based on the new nonlinear elements Covers most of the linear and nonlinear fractional-order theorems that will solve many scientific issues for researchers Closes the gap between theoretical approaches and real-world applications Provides MATLAB® and Simulink code for many of the applications in the book

**Fractional Order Processes**

Simulation, Identification, and Control

#### by **Seshu Kumar Damarla,Madhusree Kundu**

- Publisher : CRC Press
- Release : 2018-09-03
- Pages : 340
- ISBN : 0429996888
- Language : En, Es, Fr & De

The book presents efficient numerical methods for simulation and analysis of physical processes exhibiting fractional order (FO) dynamics. The book introduces FO system identification method to estimate parameters of a mathematical model under consideration from experimental or simulated data. A simple tuning technique, which aims to produce a robust FO PID controller exhibiting iso-damping property during re-parameterization of a plant, is devised in the book. A new numerical method to find an equivalent finite dimensional integer order system for an infinite dimensional FO system is developed in the book. The book also introduces a numerical method to solve FO optimal control problems. Key features Proposes generalized triangular function operational matrices. Shows significant applications of triangular orthogonal functions as well as triangular strip operational matrices in simulation, identification and control of fractional order processes. Provides numerical methods for simulation of physical problems involving different types of weakly singular integral equations, Abel’s integral equation, fractional order integro-differential equations, fractional order differential and differential-algebraic equations, and fractional order partial differential equations. Suggests alternative way to do numerical computation of fractional order signals and systems and control. Provides source codes developed in MATLAB for each chapter, allowing the interested reader to take advantage of these codes for broadening and enhancing the scope of the book itself and developing new results.

**The International Conference on Advanced Machine Learning Technologies and Applications (AMLTA2019)**

A Book

#### by **Aboul Ella Hassanien,Ahmad Taher Azar,Tarek Gaber,Roheet Bhatnagar,Mohamed F. Tolba**

- Publisher : Springer
- Release : 2019-03-16
- Pages : 960
- ISBN : 3030141187
- Language : En, Es, Fr & De

This book presents the peer-reviewed proceedings of the 4th International Conference on Advanced Machine Learning Technologies and Applications (AMLTA 2019), held in Cairo, Egypt, on March 28–30, 2019, and organized by the Scientific Research Group in Egypt (SRGE). The papers cover the latest research on machine learning, deep learning, biomedical engineering, control and chaotic systems, text mining, summarization and language identification, machine learning in image processing, renewable energy, cyber security, and intelligence swarms and optimization.

**Renewable Energy Systems**

Modelling, Optimization and Control

#### by **Ahmad Taher Azar,Nashwa Ahmad Kamal**

- Publisher : Academic Press
- Release : 2021-09-09
- Pages : 732
- ISBN : 0128203986
- Language : En, Es, Fr & De

Renewable Energy Systems: Modelling, Optimization and Control aims to cross-pollinate recent advances in the study of renewable energy control systems by bringing together diverse scientific breakthroughs on the modeling, control and optimization of renewable energy systems by leading researchers. The book brings together the most comprehensive collection of modeling, control theorems and optimization techniques to help solve many scientific issues for researchers in renewable energy and control engineering. Many multidisciplinary applications are discussed, including new fundamentals, modeling, analysis, design, realization and experimental results. The book also covers new circuits and systems to help researchers solve many nonlinear problems. This book fills the gaps between different interdisciplinary applications, ranging from mathematical concepts, modeling, and analysis, up to the realization and experimental work. Covers modeling, control theorems and optimization techniques which will solve many scientific issues for researchers in renewable energy Discusses many multidisciplinary applications with new fundamentals, modeling, analysis, design, realization and experimental results Includes new circuits and systems, helping researchers solve many nonlinear problems

**Special Functions and Analysis of Differential Equations**

A Book

#### by **Praveen Agarwal,Ravi P Agarwal,Michael Ruzhansky**

- Publisher : CRC Press
- Release : 2020-09-08
- Pages : 354
- ISBN : 1000078566
- Language : En, Es, Fr & De

Differential Equations are very important tools in Mathematical Analysis. They are widely found in mathematics itself and in its applications to statistics, computing, electrical circuit analysis, dynamical systems, economics, biology, and so on. Recently there has been an increasing interest in and widely-extended use of differential equations and systems of fractional order (that is, of arbitrary order) as better models of phenomena in various physics, engineering, automatization, biology and biomedicine, chemistry, earth science, economics, nature, and so on. Now, new unified presentation and extensive development of special functions associated with fractional calculus are necessary tools, being related to the theory of differentiation and integration of arbitrary order (i.e., fractional calculus) and to the fractional order (or multi-order) differential and integral equations. This book provides learners with the opportunity to develop an understanding of advancements of special functions and the skills needed to apply advanced mathematical techniques to solve complex differential equations and Partial Differential Equations (PDEs). Subject matters should be strongly related to special functions involving mathematical analysis and its numerous applications. The main objective of this book is to highlight the importance of fundamental results and techniques of the theory of complex analysis for differential equations and PDEs and emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Specific topics include but are not limited to Partial differential equations Least squares on first-order system Sequence and series in functional analysis Special functions related to fractional (non-integer) order control systems and equations Various special functions related to generalized fractional calculus Operational method in fractional calculus Functional analysis and operator theory Mathematical physics Applications of numerical analysis and applied mathematics Computational mathematics Mathematical modeling This book provides the recent developments in special functions and differential equations and publishes high-quality, peer-reviewed book chapters in the area of nonlinear analysis, ordinary differential equations, partial differential equations, and related applications.

**Backstepping Control of Nonlinear Dynamical Systems**

A Book

#### by **Sundarapandian Vaidyanathan,Ahmad Taher Azar**

- Publisher : Academic Press
- Release : 2020-08-15
- Pages : 532
- ISBN : 0128175834
- Language : En, Es, Fr & De

Backstepping Control of Nonlinear Dynamical Systems addresses both the fundamentals of backstepping control and advances in the field. The latest techniques explored include ‘active backstepping control’, ‘adaptive backstepping control’, ‘fuzzy backstepping control’ and ‘adaptive fuzzy backstepping control’. The reference book provides numerous simulations using MATLAB and circuit design. These illustrate the main results of theory and applications of backstepping control of nonlinear control systems. Backstepping control encompasses varied aspects of mechanical engineering and has many different applications within the field. For example, the book covers aspects related to robot manipulators, aircraft flight control systems, power systems, mechanical systems, biological systems and chaotic systems. This multifaceted view of subject areas means that this useful reference resource will be ideal for a large cross section of the mechanical engineering community. Details the real-world applications of backstepping control Gives an up-to-date insight into the theory, uses and application of backstepping control Bridges the gaps for different fields of engineering, including mechanical engineering, aeronautical engineering, electrical engineering, communications engineering, robotics and biomedical instrumentation

**Modeling and Control of Static Converters for Hybrid Storage Systems**

A Book

#### by **Fekik, Arezki,Benamrouche, Nacereddine**

- Publisher : IGI Global
- Release : 2021-09-17
- Pages : 355
- ISBN : 1799874494
- Language : En, Es, Fr & De

The energy transition initiated in recent years has enabled the growing integration of renewable production into the energy mix. Microgrids make it possible to maximize the efficiency of energy transmission from source to consumer by bringing the latter together geographically and by reducing losses linked to transport. However, the lack of inertia and the micro-grid support system makes it weak, and energy storage is necessary to ensure its proper functioning. Current storage technologies do not make it possible to provide both a large capacity of energy and power at the same time. Hybrid storage is a solution that combines the advantages of several technologies and reduces their disadvantages. Modeling and Control of Static Converters for Hybrid Storage Systems covers the modeling, control theorems, and optimization techniques that solve many scientific problems for researchers in the field of power converter control for renewable energy hybrid storage and places particular emphasis on the modeling and control of static converters for hybrid storage systems. Covering topics ranging from energy storage to power generation, this book is ideal for automation engineers, electrical engineers, mechanical engineers, professionals, scientists, academicians, master's and doctoral students, and researchers in the disciplines of electrical and mechanical engineering.

**Advances in Synchronization of Coupled Fractional Order Systems**

Fundamentals and Methods

#### by **Rafael Martínez-Guerra,Claudia Alejandra Pérez-Pinacho**

- Publisher : Springer
- Release : 2018-07-23
- Pages : 185
- ISBN : 3319939467
- Language : En, Es, Fr & De

After a short introduction to the fundamentals, this book provides a detailed account of major advances in applying fractional calculus to dynamical systems. Fractional order dynamical systems currently continue to gain further importance in many areas of science and engineering. As with many other approaches to mathematical modeling, the first issue to be addressed is the need to couple a definition of the fractional differentiation or integration operator with the types of dynamical systems that are analyzed. As such, for the fundamentals the focus is on basic aspects of fractional calculus, in particular stability analysis, which is required to tackle synchronization in coupled fractional order systems, to understand the essence of estimators for related integer order systems, and to keep track of the interplay between synchronization and parameter observation. This serves as the common basis for the more advanced topics and applications presented in the subsequent chapters, which include an introduction to the 'Immersion and Invariance' (I&I) methodology, the masterslave synchronization scheme for partially known nonlinear fractional order systems, Fractional Algebraic Observability (FAO) and Fractional Generalized quasi-Synchronization (FGqS) to name but a few. This book is intended not only for applied mathematicians and theoretical physicists, but also for anyone in applied science dealing with complex nonlinear systems.

**Fractional Order Processes**

Simulation, Identification, and Control

#### by **Seshu Kumar Damarla,Madhusree Kundu**

- Publisher : CRC Press
- Release : 2018-09-03
- Pages : 340
- ISBN : 0429996896
- Language : En, Es, Fr & De

The book presents efficient numerical methods for simulation and analysis of physical processes exhibiting fractional order (FO) dynamics. The book introduces FO system identification method to estimate parameters of a mathematical model under consideration from experimental or simulated data. A simple tuning technique, which aims to produce a robust FO PID controller exhibiting iso-damping property during re-parameterization of a plant, is devised in the book. A new numerical method to find an equivalent finite dimensional integer order system for an infinite dimensional FO system is developed in the book. The book also introduces a numerical method to solve FO optimal control problems. Key features Proposes generalized triangular function operational matrices. Shows significant applications of triangular orthogonal functions as well as triangular strip operational matrices in simulation, identification and control of fractional order processes. Provides numerical methods for simulation of physical problems involving different types of weakly singular integral equations, Abel’s integral equation, fractional order integro-differential equations, fractional order differential and differential-algebraic equations, and fractional order partial differential equations. Suggests alternative way to do numerical computation of fractional order signals and systems and control. Provides source codes developed in MATLAB for each chapter, allowing the interested reader to take advantage of these codes for broadening and enhancing the scope of the book itself and developing new results.

**Unmanned Aerial Systems**

Theoretical Foundation and Applications

#### by **Anis Koubaa,Ahmad Taher Azar**

- Publisher : Academic Press
- Release : 2021-01-21
- Pages : 650
- ISBN : 0128202777
- Language : En, Es, Fr & De

Unmanned Aerial Systems: Theoretical Foundation and Applications presents some of the latest innovative approaches to drones from the point-of-view of dynamic modeling, system analysis, optimization, control, communications, 3D-mapping, search and rescue, surveillance, farmland and construction monitoring, and more. With the emergence of low-cost UAS, a vast array of research works in academia and products in the industrial sectors have evolved. The book covers the safe operation of UAS, including, but not limited to, fundamental design, mission and path planning, control theory, computer vision, artificial intelligence, applications requirements, and more. This book provides a unique reference of the state-of-the-art research and development of unmanned aerial systems, making it an essential resource for researchers, instructors and practitioners. Covers some of the most innovative approaches to drones Provides the latest state-of-the-art research and development surrounding unmanned aerial systems Presents a comprehensive reference on unmanned aerial systems, with a focus on cutting-edge technologies and recent research trends in the area

**Introduction to Fractional Differential Equations**

A Book

#### by **Constantin Milici,Gheorghe Drăgănescu,J. Tenreiro Machado**

- Publisher : Springer
- Release : 2018-10-28
- Pages : 188
- ISBN : 3030008959
- Language : En, Es, Fr & De

This book introduces a series of problems and methods insufficiently discussed in the field of Fractional Calculus – a major, emerging tool relevant to all areas of scientific inquiry. The authors present examples based on symbolic computation, written in Maple and Mathematica, and address both mathematical and computational areas in the context of mathematical modeling and the generalization of classical integer-order methods. Distinct from most books, the present volume fills the gap between mathematics and computer fields, and the transition from integer- to fractional-order methods.

**Fractional Order Systems**

A Book

#### by **Ivo Petráš**

- Publisher : MDPI
- Release : 2019-10-29
- Pages : 114
- ISBN : 3039216082
- Language : En, Es, Fr & De

This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of real-world phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems. This Special Issue explores applications of such systems to control, synchronization, and various mathematical models, as for instance, MRI, long memory process, diffusion.

**Design, Analysis and Applications of Renewable Energy Systems**

A Book

#### by **Ahmad Taher Azar,Nashwa Ahmad Kamal**

- Publisher : Academic Press
- Release : 2021-09-09
- Pages : 760
- ISBN : 0323859917
- Language : En, Es, Fr & De

Design, Analysis and Applications of Renewable Energy Systems covers recent advancements in the study of renewable energy control systems by bringing together diverse scientific breakthroughs on the modeling, control and optimization of renewable energy systems as conveyed by leading energy systems engineering researchers. The book focuses on present novel solutions for many problems in the field, covering modeling, control theorems and the optimization techniques that will help solve many scientific issues for researchers. Multidisciplinary applications are also discussed, along with their fundamentals, modeling, analysis, design, realization and experimental results. This book fills the gaps between different interdisciplinary applications, ranging from mathematical concepts, modeling, and analysis, up to the realization and experimental work. Presents some of the latest innovative approaches to renewable energy systems from the point-of-view of dynamic modeling, system analysis, optimization, control and circuit design Focuses on advances related to optimization techniques for renewable energy and forecasting using machine learning methods Includes new circuits and systems, helping researchers solve many nonlinear problems

**Handbook of Research on Modeling, Analysis, and Control of Complex Systems**

A Book

#### by **Ahmad Taher Azar,Nashwa Ahmad Kamal**

- Publisher : Engineering Science Reference
- Release : 2020-09
- Pages : 129
- ISBN : 1799857905
- Language : En, Es, Fr & De

"This book is mainly focused on the recent achievements and applications in the field of control and analysis for complex systems with a special emphasis on how to solve various control design and/or observer design problems for nonlinear systems, interconnected systems, and singular systems and involves modeling, non-ideal systems and applications, synchronization, and control for nonlinear systems, such as mechanical, electrical, electromechanical, mechatronic, and very complex systems"--

**Fractional Calculus**

Theory

#### by **Roy Abi Zeid Daou**

- Publisher : Unknown Publisher
- Release : 2014
- Pages : 294
- ISBN : 9781634630276
- Language : En, Es, Fr & De

The first volume of this two-volume book, presents history, the mathematical modeling and the applications of fractional order systems, and contains mathematical and theoretical studies and research related to this domain. This volume is made up of 11 chapters. The first chapter presents an analysis of the Caputo derivative and the pseudo state representation with the infinite state approach. The second chapter studies the stability of a class of fractional Cauchy problems. The third chapter shows how to solve fractional order differential equations and fractional order partial differential equations using modern matrix algebraic approaches. Following this chapter, chapter four proposes another analytical method to solve differential equations with local fractional derivative operators. Concerning chapter five, it presents the extended Borel transform and its related fractional analysis. After presenting the analytical resolution methods for fractional calculus, chapter six shows the essentials of fractional calculus on discrete settings. The initialization of such systems is shown in chapter seven. In fact, this chapter presents a generalized application of the Hankel operator for initialization of fractional order systems. The last four chapters show some new studies and applications of non-integer calculus. In fact, chapter eight presents the fractional reaction-transport equations and evanescent continuous time random walks. Chapter nine shows a novel approach in the exponential integrators for fractional differential equations. Chapter ten presents the non-fragile tuning of fractional order PD controllers for integrating time delay systems. At the end, chapter eleven proposes a discrete finite-dimensional approximation of linear infinite dimensional systems. To sum up, this volume presents a mathematical and theoretical study of fractional calculus along with a stability study and some applications. This volume ends up with some new techniques and methods applied in fractional calculus. This volume will be followed up by a second volume that focuses on the applications of fractional calculus in several engineering domains.

**Fuzzy Arbitrary Order System**

Fuzzy Fractional Differential Equations and Applications

#### by **Snehashish Chakraverty,Smita Tapaswini,Diptiranjan Behera**

- Publisher : John Wiley & Sons
- Release : 2016-08-09
- Pages : 272
- ISBN : 1119004179
- Language : En, Es, Fr & De

Presents a systematic treatment of fuzzy fractional differential equations as well as newly developed computational methods to model uncertain physical problems Complete with comprehensive results and solutions, Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications details newly developed methods of fuzzy computational techniquesneeded to model solve uncertainty. Fuzzy differential equations are solved via various analytical andnumerical methodologies, and this book presents their importance for problem solving, prototypeengineering design, and systems testing in uncertain environments. In recent years, modeling of differential equations for arbitrary and fractional order systems has been increasing in its applicability, and as such, the authors feature examples from a variety of disciplines to illustrate the practicality and importance of the methods within physics, applied mathematics, engineering, and chemistry, to name a few. The fundamentals of fractional differential equations and the basic preliminaries of fuzzy fractional differential equations are first introduced, followed by numerical solutions, comparisons of various methods, and simulated results. In addition, fuzzy ordinary, partial, linear, and nonlinear fractional differential equations are addressed to solve uncertainty in physical systems. In addition, this book features: Basic preliminaries of fuzzy set theory, an introduction of fuzzy arbitrary order differential equations, and various analytical and numerical procedures for solving associated problems Coverage on a variety of fuzzy fractional differential equations including structural, diffusion, and chemical problems as well as heat equations and biomathematical applications Discussions on how to model physical problems in terms of nonprobabilistic methods and provides systematic coverage of fuzzy fractional differential equations and its applications Uncertainties in systems and processes with a fuzzy concept Fuzzy Arbitrary Order System: Fuzzy Fractional Differential Equations and Applications is an ideal resource for practitioners, researchers, and academicians in applied mathematics, physics, biology, engineering, computer science, and chemistry who need to model uncertain physical phenomena and problems. The book is appropriate for graduate-level courses on fractional differential equations for students majoring in applied mathematics, engineering, physics, and computer science.

**Non-Integer Order Calculus and its Applications**

9th International Conference on Non-Integer Order Calculus and Its Applications, Łódź, Poland

#### by **Piotr Ostalczyk,Dominik Sankowski,Jacek Nowakowski**

- Publisher : Springer
- Release : 2018-03-22
- Pages : 229
- ISBN : 3319784587
- Language : En, Es, Fr & De

This book focuses on fractional calculus, presenting novel advances in both the theory and applications of non-integer order systems. At the end of the twentieth century it was predicted that it would be the calculus of the twenty-first century, and that prophecy is confirmed year after year. Now this mathematical tool is successfully used in a variety of research areas, like engineering (e.g. electrical, mechanical, chemical), dynamical systems modeling, analysis and synthesis (e.g technical, biological, economical) as well as in multidisciplinary areas (e.g. biochemistry, electrochemistry).As well as the mathematical foundations the book concentrates on the technical applications of continuous-time and discrete-time fractional calculus, investigating the identification, analysis and control of electrical circuits and dynamical systems. It also presents the latest results.Although some scientific centers and scientists are skeptical and actively criticize the applicability of fractional calculus, it is worth breaking through the scientific and technological walls. Because the “fractional community” is growing rapidly there is a pressing need for the exchange of scientific results. The book includes papers presented at the 9th International Conference on Non-integer Order Calculus and Its Applications and is divided into three parts:• Mathematical foundations• Fractional systems analysis and synthesis• System modelingSeven papers discuss the mathematical foundations, twelve papers address fractional order analysis and synthesis and three focus on dynamical system modeling by the fractional order differential and difference equations. It is a useful resource for fractional calculus scientific community.