Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 59, Issue -, Pages 444-462Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2017.12.003
Keywords
Fractional calculus; Ordinary differential equations; Laplace transforms
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Funding
- Engineering and Physical Sciences Research Council, UK
- Engineering and Physical Sciences Research Council [1479943] Funding Source: researchfish
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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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