A Hyperaccurate Semi–Analytical Method With Error Bound Analysis for Treating Fractional Integral Equations With Functional Kernels and Variable Delays

ABSTRACT This study is concerned with treating the fractional integral equations with functional kernels and variable delays, introducing a hyperaccurate semi–analytical method based on the Stieltjes–Wigert polynomials, matrix expansions, and the Laplace transform. After analytically converting the terms in the governing equation into the matrix expansions of the Stieltjes–Wigert polynomials type at the collocation points, the method gathers these matrices into a unique matrix equation and then readily solves it by an elimination technique. The residual improvement technique is also introduced to correct the obtained solutions. The residual error bound analysis is theoretically proved via algebraical properties and the mean value theorem for fractional integral calculus, respectively. Six model equations are treated via the method, which runs on a devised computer program. Based on the outcomes, the method is straightforward to treat model equations and to encode its mainframe on a mathematical software.