Solving a System of Linear and Nonlinear Fractional Partial Differential Equations Using Homotopy Perturbation Method

摘要

This paper presents approximate analytical solutions for systems of fractional differential equations using the homotopy perturbation method. The fractional derivatives are described in the Caputo sense. The application of homotopy perturbation method, developed for differential equations of integer order, is extended to derive approximate analytical solutions of systems of fractional differential equations. The solutions of our model equations are calculated in the form of convergent series through easily computable components. Using symbolic computation, some examples are solved as illustrations. The numerical results show that the approach is accurate and easy to implement, when applied to systems of fractional differential equations. The method introduces a promising tool for solving many linear and nonlinear fractional differential equations.