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Variable order fractional systems
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DOI：10.1016/j.cnsns.2018.12.003.png)
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Abstract
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Fractional Calculus had a remarkable evolution during recent decades, and paved the way towards the definition of variable order derivatives. In the literature we find several different alternative definitions of such operators. This paper presents an overview of the fundamentals of this topic and addresses the questions of finding out which of them are reasonable according to simple criteria used for constant order fractional derivatives. This approach leads to the definitions of variable order fractional derivative based on the Grunwald-Letnikov and the Liouville formulations defined on R, as well as to the definition of a Mittag-Leffler function for variable orders, and to the application of these definitions to dynamical systems. (C) 2018 Elsevier B.V. All rights reserved.
Keywords:
Variable order
Fractional integral
Fractional derivative
Variable order linear system
Variable order Mittag-Leffler function
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