International Journal of Pure and Applied Mathematics Volume 95 No. 3 2014, 413-426 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: http://dx.doi.org/10.12732/ijpam.v95i3.9 P A ijpam.eu LAPLACE VARIATIONAL ITERATION METHOD FOR INTEGRO-DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER Toheeb A. Biala 1 , Yusuf O. Afolabi 2 , Oladapo O. Asim 3 1 Department of Mathematics University of Ilorin P.M.B. 1515 Ilorin, NIGERIA 2 Department of Mathematics Sokoto State University P.M.B. 2134 Airport Road, Sokoto, NIGERIA 3 Department of Mathematics and Physics Osun State University Osogbo, NIGERIA Abstract: 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 itera- tion 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 Key Words: variational iteration method, Laplace transform, integro-dif- ferential equation, fractional calculus, Lagrange multiplier Received: April 27, 2014 c  2014 Academic Publications, Ltd. url: www.acadpubl.eu