In the present paper, The homotopy perturbation method (HPM) is applied to obtain approximate analytical solutions of the fractional non-linear Schrodinger equations. The solutions are obtained in the form of rapidly convergent infinite series with easily computable terms. Finally, we have illustrated the ability of the method for solving fractional non linear equation by some examples.

In this paper, an anomalous advection-dispersion model involving a new general Liouville–Caputo fractional-order derivative is addressed for the first time. The series solutions of the general fractional advection-dispersion equations are obtained with the aid of the Laplace transform. The results are given to demonstrate the efficiency of the proposed formulations to describe the anomalous adv...

In this article, the fractional q-calculus and fractional q-Leibniz rule are used to generate certain infinite series expansions and transformations relating some of q-special functions of mathematical physics. Some of these expansions and transformations thus generated are known, while others appear to be new.

In this paper, the homotopy analysis transform method is used to solve the time-fractional SharmaTasso-Olever (STO) equation. This method yields an approximate analytical solution of a rapidly convergent power series with easily computable terms and produces a good approximate solution on enlarged intervals for solving the time-fractional STO equation.

We derive a series expansion for the multiparameter fractional Brownian motion. The derived expansion is proven to be rate optimal .