Analytical treatments of time-fractional seventh-order nonlinear equations via Elzaki transform

Ali，Liaqat1,2; Zou，Guang1; Li，Na1; Mehmood，Kashif2; Fang，Pan3; Khan，Adnan4

2024-04-01

10.1007/s10665-023-10326-y

Journal of Engineering Mathematics   影响因子和分区

0022-0833

1573-2703

In this article, we’ll show how to solve the time-fractional seventh-order Lax’s Korteweg–de Vries and Kaup–Kupershmidt equations analytically using the homotopy perturbation approach, the Adomian decomposition method, and the Elzaki transformation. The KdV equation is a general integrable equation with an inverse scattering transform-based solution that arises in a variety of physical applications, including surface water waves, internal waves in a density stratified fluid, plasma waves, Rossby waves, and magma flow. Fractional derivative is described in the Caputo sense. The solutions to fractional partial differential equation is computed using convergent series. The numerical computations and graphical representations of the analytical results obtained using the homotopy perturbation and decomposition techniques. Moreover, plots that are simple to grasp are used to compare the integer order and fractional-order solutions. After only a few iterations, we may easily obtain numerical results that provide us better approximations. The exact solutions and the derived solutions were observed to be very similar. The suggested methods have also acquired the highest level of accuracy. The most prevalent and convergent techniques for resolving nonlinear fractional-order partial differential issues are the applied techniques.

26A33 34A25 35A20 35Q53 Analytical techniques Caputo operator Elzaki Transform Kaup–Kupershmidt (KK) equation Lax’s Korteweg–de Vries equation

SCI ; EI

英语

第一 ; 通讯

2-s2.0-85185408029

Scopus

1.Department of Ocean Science and Engineering,Southern University of Science and Technology,Shenzhen,China
2.College of Civil Engineering and Architecture,Zhejiang University,Hangzhou,310058,China
3.Department of Maritime and Transport Technology,Delft University of Technology,Delft,2600 AA,Netherlands
4.Department of Mathematics,Abdul Wali Khan University Mardan,Mardan,23200,Pakistan

Ali，Liaqat,Zou，Guang,Li，Na,et al. Analytical treatments of time-fractional seventh-order nonlinear equations via Elzaki transform[J]. Journal of Engineering Mathematics,2024,145(1).

Ali，Liaqat,Zou，Guang,Li，Na,Mehmood，Kashif,Fang，Pan,&Khan，Adnan.(2024).Analytical treatments of time-fractional seventh-order nonlinear equations via Elzaki transform.Journal of Engineering Mathematics,145(1).

Ali，Liaqat,et al."Analytical treatments of time-fractional seventh-order nonlinear equations via Elzaki transform".Journal of Engineering Mathematics 145.1(2024).