On the Solution of Fractional Differential Equations

Abstract

This work provides a link between the fractional derivatives and ordinary derivatives by using a weighted linear combination model. We show that every fractional differ- ential equation has a dual form in the non-fractional differential equations. Solution of the non-fractional differential equation in the dual form leads to the solution of the corresponding fractional differential equation. This method reduces complex fractional problems to ordinary differential equations which opens up several ap- plications in engineering, physics and other domains. At the end, we solve several fractional differential equations found in the literature