An effective scheme for solving system of fractional Volterraxe2x80x93Fredholm integrodifferential equations based on the Mxc3xbcntzxe2x80x93Legendre wavelets Abstract   In this study, a class of wavelet techniques is used for finding approximate solutions of systems of fractional integro  differential Volterra xe2x80x93 Fredholm (FIDVF) equations based on the Muntz  Legendre wavelets (MLW). For the suggested method, operational matrices of the Riemann xe2x80x93 Liouville fractional (RLF) integral and Caputo fractional (CF) derivative operators are obtained and used for converting the system of the integral equations into a system of linear or nonlinear algebraic equations. Using the Lipschitzxe2x80x99s condition for multivariate functions and the fixed point theorem, the existence and uniqueness of the solution are shown and also convergence, stability and error bound of the solution in interval      0  ,  1      are investigated in this work. At the end, three examples are indicated and the results of the proposed method are compared with the first and second kind wavelet Chebyshev methods.

An efficient and stable Lagrangian matrix approach to Abel integral and integrodifferential equations Abstract   This article studies Abel integral equations (AIEs) and singular integrodifferential equations (SIDEs) and aims to develop two numerical schemes for them. It also emphasises on the comparative analysis of both AIEs u0026 SIDEs which is based on mainly two process namely GaussLegendre roots as collocation node points and random node points over the domain 0,1. For generating interpolating basis functions (IBF), we used Lagrangian interpolating polynomial and for orthonormal Lagrangian basis functions (OLBF), we used GramSchmidt orthogonalization algorithm, respectively. Firstly, we introduced the function approximation by using generated IBF and OLBF, then established the error bounds of these approximations. The constructed approximations by both the schemes convert the AIEs and SIDEs into the system of algebraic equations. We have also established error bounds, stability and convergence analysis of the proposed schemes by considering several mild mathematical conditions. Moreover, the stability of schemes is also established numerically. Finally, the test functions with the support of graphs clearly show the reliability and computational efficiency of the proposed methods.