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We investigate the existence of solutions for a sum-type fractional integro-differential problem via the Caputo differentiation. By using the shifted Legendre and Chebyshev polynomials, we provide a numerical method for finding solutions for the problem. In this way, we give some examples to illustrate our results.

Approximate solutions of a sum-type fractional integro-differential equation by using Chebyshev and Legendre polynomials