An efficient analytical approach for fractional equal width equations describing hydro-magnetic waves in cold plasma

Abstract In this paper, we present a coupling of homotopy perturbation technique and sumudu transform known as homotopy perturbation sumudu transform method (HPSTM). We show applicability of this method by solving fractional equal width (EW) equation, fractional modified equal width (MEW) equation and variant of fractional modified equal width (VMEW) equation. The fractional equal width equations play a key role in describing hydro-magnetic waves in cold plasma. Our aim is to study the nonlinear behaviour of plasma system and highlight the important points. We examine the ability of HPSTM to study the fractional nonlinear systems and show its supremacy over other available numerical techniques. The other key point of this investigation is to examine two important fractional equations with different nonlinearity. The HPSTM gives excellent accuracy in analogous with the numerical solution. The numerical solutions indicate that the HPSTM is a powerful technique for studying the nonlinear behavior of plasma system very precisely and accurately.