Solving Fractional Two-Dimensional Nonlinear Partial Volterra Integral Equation by Using Bernoulli Wavelet

摘要

The main aim of this paper is to use two-dimensional Bernoulli wavelet for obtaining the numerical solution of a nonlinear two-dimensional fractional partial Volterra integral equation. To do this, first, we construct the operational matrix of fractional integration as well as derivative of two-dimensional Bernoulli wavelet. Then, by applying the operational matrices and collocation method, we reduce the considered problem to a system of algebraic equations. Moreover, by preparing some theorems, we investigate the convergence analysis of the method. Finally, to show the accuracy and the applicability of the proposed method, we give some numerical examples.