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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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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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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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Communications In Nonlinear Science and Numerical Simulation

Volume

59

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444

End Page

462