Analysis of Fractional Model of Hydro-Magnetic Waves with Caputo Derivative via Natural Transform

In this article, we investigate the fractional model which deals to study the hydro-magnetic waves, acoustic-gravity waves, acoustic waves, cracked rock phenomena and thermodynamics with the help of Caputo derivative. The Natural adomian decomposition technique, which is a combination of Natural transform and a semi-analytical technique, is applied to solve the given model. The accuracy of the suggested technique is illustrated by analysing the RMS, \(L^{2}\) , and \(L^{\infty }\) errors in comparative manner with the existing methods.