An Evolutionary Numerical Method for Solving Nonlinear Fractional Fredholm-Volterra Integro-Differential Equations With a Functional Bound

Abstract

This study is concerned with solving the nonlinear fractional Fredholm-Volterra-Hammerstein integro-differential-delay equations with a functional bound, establishing a matrix-collocation method endowed with the Delannoy polynomial and matrix relations of differential and integral parts at the collocation points. The method evolves these matrix relations in terms of the reduced expansions without involving an alternative polynomial base, which makes it straight approach to the equations in question. To test its precision, a novel fractional residual error bound is proposed in the presence of the mean value theorem for fractional integral calculus and a residual function. Some numerical illustrations are materialized to discuss the efficiency and accuracy of the method compared to the others in the literature. Upon all evaluations, one can admit that the method is inventive tool for the mentioned equations and simple to devise its programme module on a mathematical software.