Operational Tau approximation for a general class of fractional integro-differential equations

in this work, an extension of the algebraic formulation of the operational tau method (otm) for the numerical solution of the linear and nonlinear fractional integro-differential equations (fides) is proposed. the main idea behind the otm is to convert the fractional differential and integral parts of the desired fide to some operational matrices. then the fide reduces to a set of algebraic equations. we demonstrate the tau matrix representation for solving fides based on arbitrary orthogonal polynomials. some advantages of using the method, errorestimation and computer algorithm are also presented. illustrative linear and nonlinear experiments are included to show the validity and applicability of the presented method. mathematical subject classification: 65m70, 34a25, 26a33, 47gxx.