Spectral numerical method for fractional order partial differential equations using Katugampola derivative

In this paper, we investigate the Telegraph fractional partial differential equations (FPDEs) with Katugampola derivative. The said derivative is a generalized form of traditional fractional order derivative. Since, for every FPDEs to find exact solution is very difficult task, therefore researchers have introduced various numerical techniques. Spectral methods based on polynomials have also considered in the last few decades very well to compute the numerical solutions for large numbers of problems of fractional order. We use shifted Jacobi polynomials to compute some numerical results for the considered class of FPDEs using Katugampola type differentiation. The adopted method is a powerful tool as needs no discretization or collocation of data. Some operational matrices are constructed on using the said polynomials to convert the considered problem to some algebraic equations. Then on using the Matlab, we present the results graphically using various fractional orders values. Some numerical examples are given to demonstrate our results.