Legendre wavelets method for the numerical solution of fractional integro-differential equations with weakly singular kernel

Mingxu Yi, Lifeng Wang, Jun Huang
2016 Applied Mathematical Modelling  
Highlights  Approximations of the fractional integro-differential equations are obtained.  Fractional integration operational matrix of Legendre wavelets is derived.  Reducing the initial problem to a system of algebraic equations.  Solving the system of algebraic equations, the approximations are got. Abstract: In this paper, numerical solutions of the linear and nonlinear fractional integrodifferential equations with weakly singular kernel where fractional derivatives are considered in
more » ... Caputo sense, have been obtained by Legendre wavelets method. The block pulse functions and their properties are employed to derive a general procedure for forming the operational matrix of fractional integration for Legendre wavelets. The application of this matrix for solving initial problem is explained. The mentioned equations are transformed into a system of algebraic equations. The error analysis of the proposed method is investigated. Finally, some numerical examples are shown to illustrate the efficiency of the approach.
doi:10.1016/j.apm.2015.10.009 fatcat:g3lwxfrnpnf3jpzpmaoos5pmii