On Some New Properties of Fractional Derivatives With Mittag-Leffler Kernel
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Date
2018
Authors
Baleanu, Dumitru
Fernandez, Arran
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Publisher
Elsevier Science BV
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Abstract
We establish a new formula for the fractional derivative with Mittag-Leffler kernel, in the form of a series of Riemann-Liouville fractional integrals, which brings out more clearly the non-locality of fractional derivatives and is easier to handle for certain computational purposes. We also prove existence and uniqueness results for certain families of linear and nonlinear fractional ODEs defined using this fractional derivative. We consider the possibility of a semigroup property for these derivatives, and establish extensions of the product rule and chain rule, with an application to fractional mechanics. (C) 2017 Elsevier B.V. All rights reserved.
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Keywords
Fractional Calculus, Ordinary Differential Equations, Laplace Transforms
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Citation
Baleanu, Dumitru; Fernandez, Arran, "On some new properties of fractional derivatives with Mittag-Leffler kernel", Communications In Nonlinear Science and Numerical Simulation, Vol. 59, pp. 444-462, (2018)
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Source
Communications In Nonlinear Science and Numerical Simulation
Volume
59
Issue
Start Page
444
End Page
462