Computational Approach for Two-Dimensional Fractional Integro-Differential Equations

In this article, we have proposed two numerical schemes, namely scheme-I and scheme-II to find numerical solution of two-dimensional fractional integro-differential equations (FIDEs) based on Legendre polynomial (LP) as a basis functions and interpolating basis functions (IBF) respectively. We have transformed the proposed models with initial and Dirichlet boundary conditions into fractional integro-differential equations (FIDEs). Finally, the designed algorithm has converted the FIDEs into generalized algebraic Sylvester equations. The proposed schemes are tested on several test functions with respect to absolute-error, \(L_{\infty }\) $L_{\infty }$ -error and CPU time to validate the desired accuracy and efficiency of the schemes. The error analysis of the approximate solution is provided and the stability of the schemes are verified numerically by adding some noisy data in source term. A comparative study is provided between the proposed schemes and an existing scheme.