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Variable Order and Distributed Order Fractional Operators
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.
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
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.
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
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
A solution to the fundamental linear fractional order differential equation.
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
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
Dynamics and Control of Initialized Fractional-Order Systems
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
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
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