A Numerical Method for Fractional Pantograph Delay Integro-Differential Equations on Haar Wavelet

The main objective of this research work is devoted to study the solution of fractional pantograph delay integro-differential equations based on Haar wavelet collocation (HWC) technique. Through HWC algorithm, first we reduce the underlying equations to a system of algebraic equations. After getting a system of equations, Gauss elimination method is used for the solution of the mentioned problem. Under the techniques of functional analysis, we derive the necessary conditions for the existence and uniqueness of at most one solution of the considered problem. With the help of examples taken from the literature, we investigate the validation and convergence of the HWC method. In these examples, we compare the exact and approximate solutions for different fractional orders. Through tables, errors are calculated for different nodal points, we also compare the exact and approximate solutions for different fractional orders. © 2021, The Author(s), under exclusive licence to Springer Nature India Private Limited part of Springer Nature.