A new and efficient numerical method based on shifted fractional‐order Jacobi operational matrices for solving some classes of two‐dimensional nonlinear fractional integral equations

Abstract

The aim of this paper is to present a new and efficient numerical method to approximate the solutions of two-dimensional nonlinear fractional Fredholm and Volterra integral equations. For this aim, the two-variable shifted fractional-order Jacobi polynomials are introduced and their operational matrices of fractional integration and product are derived. These operational matrices and shifted fractional-order Jacobi collocation method are utilized to reduce the understudy equations to systems of nonlinear algebraic equations. Then, the arising systems can be solved by the Newton method. Discussion on the convergence analysis and error bound of the proposed method is presented. The efficiency, accuracy, and validity of the presented method are demonstrated by its application to three test examples and by comparing our results with the results obtained by existing numerical methods in the literature recently.

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