Numerical solutions of integrodifferential equations of Fredholm operator type in the sense of the Atangana–Baleanu fractional operator

Abstract

In this article, by popularization of the reproducing kernel Hilbert space method in the sense of the Atangana–Baleanu fractional operator; set of first-order integrodifferential equations are solved with respect to Fredholm operator and initial conditions of optimality. The solvability approach based on use of the generalized Mittag–Leffler function in order to avoid nonsingular and nonlocal kernel functions appears in the classical fractional operator's. The procedure of solution is studied and described in details under some hypotheses, which provides the theoretical structure behind the utilized numerical method. Indeed, error analysis and convergence of numerical solution for the identification of the method is introduced in Hilbert space. In this analysis, some computational results and graphical representations are presented to demonstrated the suitability and portability of the utilized new fractional operator. Finally, the gained results reach to that; the utilized method is simple, direct, and powerful tool in finding numerical solutions for considered fractional equations.