Numerical Solutions of Fractional Integrodifferential Equations of Bratu Type by Using CAS Wavelets

Abstract

A numerical method based on the CAS wavelets is presented for the fractional integrodifferential equations of Bratu type. The CAS wavelets operational matrix of fractional order integration is derived. A truncated CAS wavelets series together with this operational matrix is utilized to reduce the fractional integrodifferential equations to a system of algebraic equations. The solution of this system gives the approximation solution for the truncated limited $2^k(2M+1)$. The convergence and error estimation of CAS wavelets are also given. Two examples are included to demonstrate the validity and applicability of the approach.