New results on existence in the framework of Atangana–Baleanu derivative for fractional integro-differential equations

By Chokkalingam Ravichandran, K. Logeswari, Fahd Jarad. Chaos, Solitons & Fractals, 2019

160 citations recorded by the source corpus.

Abstract In this article, we consider integro-differential equations involving the recently explored Atangana–Baleanu fractional derivatives which contain the generalized Mittag-Leffler functions in their kernels. Utilizing fixed point techniques, we examine the existence and uniqueness of solutions to such equations in Banach spaces. Moreover, we consider an example and investigate numerical outcomes for various values of the fractional order. Then, we consider the stability of the tackled integro-differential equation in the frame of Ulam.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/6ae36429531fc4986e872938572e68861b8765d7

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

A study on fractional predator–prey–pathogen model with Mittag–Leffler kernel‐based operators (2020, methodology): “…method [33], Variational approach [34, 35], q-homotopy analysis method [36], Laplace HPM [37, 36], Numerical schemes [38, 39], fixed point technique [40, 41], predictor–corrector, and spectral scheme [42, 43], the Laplace transform method [44, 45] and Mittag–Leffler kernel-based operators [46, 47].”
Numerical investigations on COVID‐19 model through singular and non‐singular fractional operators (2020, background): “Here, we survey briefly the essential preliminaries of singular and non-singular operators for this study [28, 34, 35, 38, 39, 43, 45].”