Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

A Predictor-Corrector Algorithm for IVPs in Frame of Generalized Fractional Operator With Mittag-Leffler Kernels

Version 1 : Received: 5 April 2022 / Approved: 6 April 2022 / Online: 6 April 2022 (11:38:48 CEST)

How to cite: Slimane, I.; Odibat, Z.; Baleanu, D. A Predictor-Corrector Algorithm for IVPs in Frame of Generalized Fractional Operator With Mittag-Leffler Kernels. Preprints 2022, 2022040045 (doi: 10.20944/preprints202204.0045.v1). Slimane, I.; Odibat, Z.; Baleanu, D. A Predictor-Corrector Algorithm for IVPs in Frame of Generalized Fractional Operator With Mittag-Leffler Kernels. Preprints 2022, 2022040045 (doi: 10.20944/preprints202204.0045.v1).

Abstract

This study develops a predictor-corrector algorithm for the numerical simulation of IVPs involving singular generalized fractional derivatives with Mittag-Leffler kernels. The proposed algorithm converts the considered IVP into a Volterra-type integral equation and then uses Trapezoidal rule to obtain approximate solutions. Numerical approximate solutions of some singular generalized fractional derivative with Mittag-Leffler kernels models have been presented to demonstrate the efficiency and accuracy of the proposed algorithm. The algorithm describes the influence of the fractional derivative parameters on the dynamics of the studied models. The suggested method is expected to be effectively employed in the field of simulating generalized fractional derivative models

Keywords

Fractional differential equation; singular generalized fractional derivative; Mittag-Leffler kernel; predictor-corrector algorithm; numerical solution

Subject

MATHEMATICS & COMPUTER SCIENCE, Computational Mathematics

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