The Modified Variational Iteration Method for Solving Differential Equations with Fractional Order

Abstract

In this thesis we give a brief history and definition of fractional calculus and we discuss standard approaches to problems of fractional derivatives and fractional integrals namely the Riemann-Liouville, the Caputo respectively. Then we introduce some basic definitions and facts on partial fractional calculus theory and fixed-points theory, we give some generalizations of Gronwall’s lemmas for two independent variables. Also we concern by existence of solutions to fractional order partial functional differential equations. Finally we apply the modified variational iteration method to give analytical solutions of fractional differential equations.