The construction of operational matrix of fractional integration for solving fractional differential and integro-differential equations

This study intends to present a general formulation for the hybrid Jacobi and block pulse operational matrix of fractional integral operator in order to solve fractional differential and integro-differential equations. First, we define hybrid Jacobi polynomials and block pulse functions as an orthogonal basis for function approximation. Then, we construct the operational matrix of fractional integration for these hybrid functions. With the combined features of these hybrid functions and their operational matrix of fractional integration, the governing equations that take the form of fractional differential and integro-differential equations are reduced to a system of algebraic equations. Illustrative examples are given to demonstrate the validity and reliability of the present technique.