Two-Variable Jacobi Polynomials for Solving Some Fractional Partial Differential Equations (Journal of Computational Mathematics, 2021)
Two-variable Jacobi polynomials, as a two-dimensional basis, are applied to solve a classof temporal fractional partial differential equations. The fractional derivative operators arein the Caputo sense. The operational matrices of the integration of integer and fractionalorders are presented. Using these matrices together with the Tau Jacobi method convertsthe main problem into the corresponding system of algebraic equations. An error bound isobtained in a two-dimensional Jacobi-weighted Sobolev space. Finally, the efficiency of theproposed method is demonstrated by implementing the algorithm to several illustrativeexamples. Results will be compared with those obtained from some existing methods.