Soliton solutions for nonlinear variable-order fractional Korteweg-de Vries(KdV)equation arising in shallow water waves  

作　　者：Umair Ali Hijaz Ahmad Hanaa Abu-Zinadah 

机构地区：[1]Department of Applied Mathematics and Statistics,Institute of Space Technology,P.O.Box 2750,Islamabad 44000,Pakistan [2]Near East University,Operational Research Center in Healthcare,Near East Boulevard,PC:99138 Nicosia/Mersin 10,Turkey [3]Section of Mathematics,International Telematic University Uninettuno,Corso Vittorio Emanuele II,39,00186 Roma,Italy [4]University of Jeddah,College of Science,Department of Statistics,Jeddah,Saudi Arabia

出　　处：《Journal of Ocean Engineering and Science》2024年第1期50-58,共9页海洋工程与科学（英文）

摘　　要：Nonlinear fractional differential equations provide suitable models to describe real-world phenomena and many fractional derivatives are varying with time and space.The present study considers the advanced and broad spectrum of the nonlinear(NL)variable-order fractional differential equation(VO-FDE)in sense of VO Caputo fractional derivative(CFD)to describe the physical models.The VO-FDE transforms into an ordinary differential equation(ODE)and then solving by the modified(G/G)-expansion method.For ac-curacy,the space-time VO fractional Korteweg-de Vries(KdV)equation is solved by the proposed method and obtained some new types of periodic wave,singular,and Kink exact solutions.The newly obtained solutions confirmed that the proposed method is well-ordered and capable implement to find a class of NL-VO equations.The VO non-integer performance of the solutions is studied broadly by using 2D and 3D graphical representation.The results revealed that the NL VO-FDEs are highly active,functional and convenient in explaining the problems in scientific physics.

关 键 词：Space-time VO fractional KdV equation modified(G′/G)-expansion method VO Caputo fractional derivative generalized Riccati equation 

分 类 号：O17[理学—数学]