The heat equation is parabolic partial differential equation and occurs in the characterization
of diffusion progress. In the present work, a new fractional operator based on the Rabotnov …

This article applies efficient methods, namely, modified decomposition method and new
iterative transformation method, to analyze a nonlinear system of Korteweg–de Vries …

Abstract Very recently, Yang, Abdel-Aty and Cattani (2019) introduced a new and intersting
fractional derivative operator with non-singular kernel involving Rabotnov fractional …

In applied sciences and engineering, partial differential equations (PDE) of integer and non-
integer order play a crucial role. It can be challenging to determine these equations' exact …

In this paper, we present new ideas for the implementation of homotopy asymptotic method
(HAM) to solve systems of nonlinear fractional differential equations (FDEs). An effective …

In the present article, fractional-order heat and wave equations are solved by using the
natural transform decomposition method. The series form solutions are obtained for …

This article investigates the seventh-order Lax's Korteweg–de Vries equation using the Yang
transform decomposition method (YTDM) and the homotopy perturbation transform method …

Purpose The classical integer derivative diffusionmodels for fluid flow within a channel of
parallel walls, for heat transfer within a rectangular fin and for impulsive acceleration of a …

In wave theory, the higher dimensional non-linear models are very important to define the
physical phenomena of waves. Herein study we have built the various solitons solutions of …

Abstract The physics of the (4+ 1)-dimensional Fokas equation follows necessarily from the
physical nature of the Kadomtsev–Petviashvili and Davey-Stewartson equations in wave …