Orthonormal Chelyshkov polynomials for multi-term time fractional two-dimensional telegraph type equations

Abstract

In this study, multi-term time fractional 2D telegraph type equations, as a new category of fractional differential equations, are introduced. The orthonormal Chelyshkov polynomials are used as basis functions to generate a collocation method for such equations. In this way, new results are obtained for the fractional and classical derivatives of these polynomials. In the proposed method, by representing the problem’s solution in terms of the orthonormal Chelyshkov polynomials (with unknown coefficients) and applying the extracted matrices, along with the collocation method, a solution is elicited for the problem under consideration. In fact, finding the solution of the initial problem turns into assigning the expansion coefficients through solving a system of algebraic equations. The accuracy of the proposed method is numerically checked with several examples.