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In this paper, we investigate approximate solutions for nonlinear Fredholmintegro-differential equations of fractional order. We present an operationalTau method by obtaining the Tau matrix representation. We solve a special classof nonlinear Fredholm integro-differential equations based on Legendre-Taumethod. By using the Sobolev inequality and some of Banach algebra properties,we prove that our proposed method converges to the exact solution in L^2-norm.

The convergence of operational Tau method for solving a class of nonlinear Fredholm fractional integro-differential equations on Legendre basis