A NOVEL METHOD FOR LINEAR AND NONLINEAR FRACTIONAL VOLTERRA INTEGRAL EQUATIONS VIA CUBIC HAT FUNCTIONS

Abstract

In this study, a new numerical algorithm is proposed for solving a class of nonlinear fractional Volterra integral equations of the second kind based on our newly constructed hat functions. New functions that are called cubic hat functions (CHFs) and operational matrices of fractional order integration of these functions are applied. In a new numerical approach, the fractional order operational matrix of CHFs and the powers of weakly singular kernels of integral equations are handed down as a structure for converting the principal problem into a number of systems containing three-variable polynomial equations. Also, error analysis, convergence analysis of this method and convergence rate are investigated. In the last part, the high precision of the utilized method is shown with three examples. In addition, comparisons with Jacobi spectral Galerkin and modified hat functions methods demonstrate the improved performance of the presented approach.