Nonlinear fractional partial coupled systems approximate solutions through operational matrices approach
In this article, the numerical method based on operational matrices of fractional order derivatives and integrals in the Caputo and Riemann-Liouville senses of two-parametric orthogonal shifted Jacobi polynomials is proposed for studying the approximate solutions for a generalized class of fractional order partial differential equations. The technique is extended herein to generalized classes of fractional order coupled systems having mixed partial derivatives terms. One salient aspect of this article is the development of a new operational matrix for mixed partial derivatives in the sense of Caputo. The validity of the method is established by comparing our simulated results with literature solutions obtained otherwise, yielding negligible errors. Furthermore, as a result of the comparative study, some results presented in the literature are extended and improved in the investigation herein.