A novel numerical approach for solving fractional order differential equations using hybrid functions

This article presents a novel numerical method for seeking the numerical solutions of fractional order differential equations using hybrid functions consisting of block-pulse functions and Taylor polynomials. The fractional integrals operational matrix of the hybrid function is conducted through projecting the hybrid functions onto block-pulse functions. Then, the fractional order differential equations are converted to a set of algebraic equations via the derived operational matrix. Then, the numerical solutions are obtained via solving the algebraic equations. Moreover, we perform error analysis of the algorithm and gives the upper bound of absolute error. Finally, numerical examples are given to show the effectiveness of the proposed method.