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The main purpose of this work is to present an efficient approximate approach for solving linear systems of fractional integro-differential equations based on a new application of Taylor expansion. Using the mth-order Taylor polynomial for unknown functions and employing integration method the given system of fractional integro-differential equations will be converted into a system of linear equations with respect to unknown functions and their derivatives. The solutions of this system yield the approximate solutions of fractional integro-differential equations system. The Riemann-Liouville fractional derivative is applied in calculations. An error analysis is discussed as well. The accuracy and the efficiency of the suggested method is illustrated by considering five numerical examples.

We combine the Adomian decomposition method (ADM) and Adomian’s asymptotic decomposition method (AADM) for solving Riccati equations. We investigate the approximate global solution by matching the near-field approximation derived from the Adomian decomposition method with the far-field approximation derived from Adomian’s asymptotic decomposition method for Riccati equations and in such cases when we do not find any region of overlap between the obtained approximate solutions by the two proposed methods, we connect the two approximations by the Padé approximant of the near-field approximation. We illustrate the efficiency of the technique for several specific examples of the Riccati equation for which the exact solution is known in advance.