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Discontinuity, Nonlinearity, and Complexity 14(2) (2025) 315--324 | DOI:10.5890/DNC.2025.06.006

Ibrahim Slimane$^{1}$, Zaid Odibat$^{2}$, Dumitru Baleanu$^{3,4}$

$^{1}$ Faculty of Exact Sciences and Informatics, Abdelhamid Ibn Badis University of Mostaganem P. O. Box 227, 27000 Mostaganem, Algeria

$^{2}$ Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Salt 19117, Jordan

$^{3}$ Department of Computer Science and Mathematics, Lebanese American University, Beirıt, Lebanon

$^{4}$ Institute of Space Sciences, Magurele-Bucharest, Romania

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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.

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