Wavelet‎-based numerical ‎method‎ ‎‎‎‎for solving fractional integro-differential equation with a weakly singular ‎kernel

Abstract

This paper describes and compares application of wavelet basis and Block-Pulse functions (BPFs) for solving fractional integro-differential equation (FIDE) with a weakly singular kernel‎. ‎First‎, ‎a collocation method based on Haar wavelets (HW)‎, ‎Legendre wavelet (LW)‎, ‎Chebyshev wavelets (CHW)‎, ‎second kind Chebyshev wavelets (SKCHW)‎, ‎Cos and Sin wavelets (CASW) and BPFs are presented for driving approximate solution FIDEs with a weakly singular kernel‎. ‎Error estimates of all proposed numerical methods are given to test the convergence and accuracy of the method‎. ‎A comparative study of accuracy and computational time for the presented techniques is given‎.