Modified fractional decomposition method having integral w.r.t (dξ)α(dξ)α

In this paper, a novel analytical method is proposed for differential equations with time-fractional derivative. This method is based on the famous Adomian decomposition method and the modified Riemann-Liouville derivative. The fractional derivatives are considered in the Jumarie sense. However, all the previous works avoid the term of fractional derivative and handle them as a restricted variation. In order to overcome this shortcoming, a fractional decomposition method is proposed with modified Riemann-Liouville derivative. This method is a more efficient approach to solve the fractional differential equations. Several illustrative examples are given to demonstrate the effectiveness of the present method.