An operational matrix based on Chelyshkov polynomials for solving multi-order fractional differential equations

The main purpose of this work is to use the Chelyshkov-collocation spectral method for the solution of multi-order fractional differential equations under the supplementary conditions. The method is based on the approximate solution in terms of Chelyshkov polynomials with unknown coefficients. The framework is using transform equations and the given conditions into the matrix equations. By merging these results, a new operational matrix of fractional-order derivatives in Caputo sense is constructed. Finally, numerical results are included to show the validity and applicability of the method and comparisons are made with existing results.