A wavelet collocation method based on Gegenbauer scaling function for solving fourth-order time-fractional integro-differential equations with a weakly singular kernel

Abstract

A high resolution wavelet collocation method based on Gegenbauer polynomials is proposed for the solution of fourth-order time-fractional integro-differential equations (FTFIDE) with a weakly singular kernel. A Riemann-Liouville fractional integral operator for the Gegenbauer scaling function (RLFIO-G) is constructed using the definition of Riemann-Liouville (R-L) operator with the aid of Gegenbauer scaling function. The application of Gegenbauer scaling function and RLFIO-G to FTFIDE gives a system of linear algebraic equations, which can be quickly solved for unknown coefficients. With the aid of these coefficients, we get the approximate solution. We have also established the convergence analysis of the proposed method. We have tested the presented method on some numerical examples to demonstrate the accuracy. Moreover, we have compared the developed method with the existing method to conclude the superiority of the proposed method.