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Fractional Bernstein Operational Matrices For Solving Integro-Differential Equations Involved By Caputo Fractional Derivative, M.H.T. Alshbool, Mutaz Mohammad, Osman Isik, Ishak Hashim

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The present work is devoted to developing two numerical techniques based on fractional Bernstein polynomials, namely fractional Bernstein operational matrix method, to numerically solving a class of fractional integro-differential equations (FIDEs). The first scheme is introduced based on the idea of operational matrices generated using integration, whereas the second one is based on operational matrices of differentiation using the collocation technique. We apply the Riemann–Liouville and fractional derivative in Caputo’s sense on Bernstein polynomials, to obtain the approximate solutions of the proposed FIDEs. We also provide the residual correction procedure for both methods to estimate the absolute errors. Some results …