Solving Fractional Initial Value Problems by Using Hybrid Series

Abstract

In this paper, we suggest a new method for solving fractional initial value problems of different fractional orders. We call it hybrid Series Solution (Fractional with power, Fractional with fractional, Fractional with power and fractional). The main difference between Caputo and Riemann – Liouville formulas for the fractional derivatives as mentioned. The paper focuses on finding the exact solution of Bagley-Torvik equation and other nonhomogeneous fractional differential equations, illustrated by some Theorems and examples