Numerical solution of fractional Volterra-Fredholm integro-differential equations with mixed boundary conditions via Chebyshev wavelet method

Abstract

ABSTRACTIn this paper, the fourth kind Chebyshev wavelets collocation method (FCWM) is applied for solving a class of fractional Volterra-Fredholm integro-differential equations with mixed boundary conditions. Fractional integral formula of a single Chebyshev wavelet in the Riemann-Liouville sense is derived by means of shifted Chebyshev polynomials of the fourth kind. Moreover, upper bound of error of the fourth kind Chebyshev wavelets expansion is given. Based on the collocation technique, the fourth kind Chebyshev wavelets together with Gaussian integration are used to reduce the problem to the solution of a system of algebraic equations. During the process of establishing the expression of the solution, the boundary conditions are taken into account automatically, which is very convenient for solving the problem under consideration. Some examples are provided to confirm the reliability and effectiveness of the proposed method.