Numerical Solution of Fractional Integro-differential Equations with Weakly Singular Kernels via Bernstein Polynomial

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This paper is concerned with obtaining approximate numerical solutions of a class of fractional Volterra integro-differential equations with weakly singular kernels which using Bernstein Polynomials as basis in collocation methods(BPCM). The approximate solution is obtained by expanding the functions in terms of Bernstein Polynomial, whose unknown coefficients are determined by solving final system of linear equations. The convergence analysis of the proposed method are taken into consideration and Numerical examples are included to confirm the efficiency and accuracy of the method.