Existence and Uniqueness of Solutions for Fractional Integro-Differential Equations and Their Numerical Solutions

In this paper, we investigate the existence and uniqueness of solution for a multi-term fractional integro-differential problem with nonlocal four-point fractional boundary conditions via the Caputo differentiation. We obtain operational matrix of Riemann–Liouville fractional integral operator of Bernstein polynomials and investigate the numerical solutions of the problem by using the collocation method. By appling these matrices fractional integro-differential equations convert to a linear system of equations. In this way, we give some examples to illustrate our results. The numerical method is computer oriented and produces very accurate and stable numerical results. © 2020, Springer Nature India Private Limited.