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Variable Order and Distributed Order Fractional Operators

- C. Lorenzo, T. Hartley
- Mathematics
- 1 February 2002

Many physical processes appear to exhibit fractional order behavior thatmay vary with time or space. The continuum of order in the fractionalcalculus allows the order of the fractional operator to be… Expand

Generalized functions for the fractional calculus.

- C. Lorenzo, T. Hartley
- Medicine, Mathematics
- Critical reviews in biomedical engineering
- 2008

Previous papers have used two important functions for the solution of fractional order differential equations, the Mittag-Leffler functionE(sub q)[at(exp q)](1903a, 1903b, 1905), and the F-function… Expand

Chaos in a fractional order Chua's system

- T. Hartley, C. Lorenzo, H. K. Qammer
- Mathematics
- 1 August 1995

This brief studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. By varying the total system order… Expand

Initialization, conceptualization, and application in the generalized (fractional) calculus.

- C. Lorenzo, T. Hartley
- Mathematics, Medicine
- Critical reviews in biomedical engineering
- 2007

This paper provides a formalized basis for initialization in the fractional calculus. The intent is to make the fractional calculus readily accessible to engineering and the sciences. A modified set… Expand

Initialized Fractional Calculus

- C. Lorenzo, T. Hartley
- Engineering
- 1 February 2000

This paper demonstrates the need for a nonconstant initialization for the fi'actional calculus and establishes a basic definition set for the initialized fractional differintegTal. This definition… Expand

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- 7
- PDF

A solution to the fundamental linear fractional order differential equation.

- T. Hartley, C. Lorenzo
- Medicine, Mathematics
- Critical reviews in biomedical engineering
- 2008

This paper provides a solution to the fundamental linear fractional order differential equation, namely, cdtqx(t) + ax(t) = bu(t). The impulse response solution is shown to be a series, named the… Expand

Fractional System Identification: An Approach Using Continuous Order-Distributions

- T. Hartley, C. Lorenzo
- Mathematics
- 1 November 1999

The NASASTIProgram Office... in ProfileSinceits founding, NASA has been dedicated to • CONFERENCE PUBLICATION.Collectedthe advancement of aeronautics and space papers from scientific and technical… Expand

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- 4
- PDF

Dynamics and Control of Initialized Fractional-Order Systems

- T. Hartley, C. Lorenzo
- Mathematics
- 1 July 2002

Due to the importance of historical effects in fractional-order systems,this paper presents a general fractional-order system and control theorythat includes the time-varying initialization response.… Expand

Initialization in fractional order systems

- C. Lorenzo, T. Hartley
- Mathematics
- European Control Conference (ECC)
- 1 September 2001

This paper proves the requirement of a time-varying initialization for fractional differential equations. This then requires a new definition for the fractional differintegral that includes the… Expand

Initialization of Fractional-Order Operators and Fractional Differential Equations

- C. Lorenzo, T. Hartley
- Mathematics
- 24 January 2008

It has been known that the initialization of fractional operators requires time-varying functions, a complicating factor. This paper simplifies the process of initialization of fractional… Expand