On some new properties of fractional derivatives with Mittag-Leffler kernel

By Dumitru Băleanu, Arran Fernandez. Communications in nonlinear science & numerical simulation, 2017

319 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/683b7507d9938c331eb019cbe715c9f8c6b62c84

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In Applied Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

On a Fractional Operator Combining Proportional and Classical Differintegrals (2020, background): “The equivalence of these two expressions for the fractional integral operator is clear from the series formula approach of [9,21].”
Integral inequalities for a fractional operator of a function with respect to another function with nonsingular kernel (2020, methodology): “There are two important models of fractional calculus which have been defined by integrals similar to (1) but with Mittag-Leffler (ML) functions in the kernel, namely the Atangana–Baleanu and Prabhakar models [9, 10].”
On Fractional Operators and Their Classifications (2019, methodology): “• A model proposed by Atangana and Baleanu [25], which was defined more rigorously in [36] and whose applications have been discussed in [37–39], utilises an integral transform with a one-parameter Mittag-Leffler function (Eν(z) = ∑n=0 zn Γ(nν+1) for Re(ν) > 0) in the kernel and an arbitrary normali”