Collocation method for fractional differential equations using hybrid fractional-order Chelyshkov functions

In this paper, we introduce a new numerical method based on the hybrid of fractional-order Chelyshkov functions and block-pulse functions for solving fractional differential equations. The fractional derivatives are considered in the Caputo sense. The exact formula for the Riemann-Liouville fractional integral of these basis functions is derived via the Laplace transform. This formula, together with the spectral collocation method are used to reduce the main problem to a system of algebraic equations. The convergence of the introduced method is discussed. Several illustrative examples are included to demonstrate the accuracy and applicability of the proposed method.