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Fractional Integro-Differential Equations (FIDEs) arise in the mathematical modelling of physical phenomena and play an important role in various branches of science and engineering. With He’s variational iteration method, it is possible to obtain exact or better approximate solutions of differential equations. This paper is concerned with the solution of FIDEs by the variational iteration method via the Laplace transform. In this approach, a correction functional is constructed by a general Lagrange multiplier, which is determined by using the Laplace transform with the variational theory. The results of applying this method to the studied FIDEs show the high accuracy, simplicity and efficiency of the approach. AMS Subject Classification: 65L03, 45J05

LAPLACE VARIATIONAL ITERATION METHOD FOR INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER