Sparse wavelet Galerkin method: Application for fractional Pantograph problem

Abstract

The multiwavelets Galerkin method is utilized to solve the fractional Pantograph equation. The method is based on rendering the desired problem into the equivalent integral equation with a weakly singular kernel (fractional integral equation). In this paper, for the first time, the wavelet properties are considered to solve and reduce the computational load for these equations. Compared to the use of other bases, even wavelets generated by a single generator, particularly Alpert’s multiwavelets, have been found to exhibit superior efficiency due to their unique properties. Our investigation supports the theoretical finding. The illustrative examples are also reported, demonstrating the accuracy and flexibility of the method.