Efficient method for solving nonlinear weakly singular kernel fractional integro-differential equations

Author:

Ameen Ismail Gad1,Baleanu Dumitru2,Hussien Hussien Shafei1

Affiliation:

1. Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt

2. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

Abstract

<abstract><p>This paper introduced an efficient method to obtain the solution of linear and nonlinear weakly singular kernel fractional integro-differential equations (WSKFIDEs). It used Riemann-Liouville fractional integration (R-LFI) to remove singularities and approximated the regularized problem with a combined approach using the generalized fractional step-Mittag-Leffler function (GFSMLF) and operational integral fractional Mittag matrix (OIFMM) method. The resulting algebraic equations were turned into an optimization problem. We also proved the method's accuracy in approximating any function, as well as its fractional differentiation and integration within WSKFIDEs. The proposed method was performed on some attractive examples in order to show how their solutions behave at various values of the fractional order $ \digamma $. The paper provided a valuable contribution to the field of fractional calculus (FC) by presenting a novel method for solving WSKFIDEs. Additionally, the accuracy of this method was verified by comparing its results with those obtained using other methods.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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