Romanovski–Jacobi polynomials for the numerical solution of multi-dimensional multi-order time fractional telegraph equations

Abstract

In this paper, the one- and two-dimensional multi-order time fractional telegraph equations are introduced. Two collocation methods based on the one- and two-dimensional Romanovski–Jacobi polynomials are proposed to solve them. In this way, some operational matrices related to the classical and fractional derivatives of these polynomials are achieved at first. Then, the solution of the problem under consideration is approximated by a finite expansion of these polynomials with unknown coefficients. Next, an algebraic system of equations is created in terms of the expansion coefficients by applying the derived operational matrices and the collocation technique. Eventually, by solving this system and determining the expressed coefficients, a solution for the multi-order time fractional telegraph equation under consideration is obtained. The correctness of the developed schemes are checked by solving some examples.

Keywords

• Romanovski–Jacobi polynomials
• Multi-order time fractional telegraph equations
• Caputo fractional derivative