A numerical algorithm for a class of nonlinear fractional Volterra integral equations via modified hat functions

Abstract

A numerical algorithm via a modified hat functions (MHFs) has been proposed to solve a class of nonlinear fractional Volterra integral equations of the second kind. A fractional-order operational matrix of integration is introduced. In a new methodology, the operational matrices of MHFs and the powers of weakly singular kernels of integral equations are used as a structure for transforming the main problem into a number of systems consisting of two equations for two unknowns. Relative errors for the approximated solutions are investigated. Convergence analysis of the proposed method is evaluated and convergence rate is addressed. Finally, the extraordinary accuracy of the utilized approach is illustrated by a few examples. The results, absolute and relative errors are illustrated in some tables and diagrams. In addition, a comparison is made between the absolute errors obtained by the proposed method and two other methods; one uses a hybrid approach and the other applies second Chebyshev wavelet.