The analytic solution of the fractional Rosenau--Hyman model in
Liouville-Caputo sense
Abstract
The purpose of this work is to achieve the analytic solution of
non-linear Liouville-Caputo fractional initial value problem including
time fractional Rosenau–Hyman equation by means of ARA transform and
iterative method. First of all, ARA transform is employed to reduce the
problem into a simpler one. Then the series solution of the non-linear
fractional initial value problem is acquired by applying iterative
method which leads to the analytic solution of the Rosenau–Hyman
equation (RHE) with initial condition. The obtained results verify that
the combination of ARA transform with iterative method produces an
effective method to tackle with non-linear fractional problems.