[HTML][HTML] A survey of (2+ 1)-dimensional KdV–mKdV equation using nonlocal Caputo fractal–fractional operator

A Jamal, A Ullah, S Ahmad, S Sarwar, A Shokri - Results in Physics, 2023 - Elsevier
Abstract We analyze the nonlinear (2+ 1)-dimensional KdV–mKdV equation with Caputo
fractal–fractional operator. Some theoretical features are demonstrated via fixed point …

TRAVELING WAVE SOLUTION OF FRACTAL KdV-BURGERS–KURAMOTO EQUATION WITHIN LOCAL FRACTIONAL DIFFERENTIAL OPERATOR

J Sun - Fractals, 2021 - World Scientific
In this work, space-time fractal model about nonlinear KdV-Burgers–Kuramoto (NKBK)
equation which describes nonlinear physical phenomena and involves instability …

Nonlinear dynamic behaviors of the fractional (3+ 1)-dimensional modified Zakharov–Kuznetsov equation

KJ Wang, P Xu, F Shi - Fractals, 2023 - World Scientific
This paper derives a new fractional (3+ 1)-dimensional modified Zakharov–Kuznetsov
equation based on the conformable fractional derivative for the first time. Some new types of …

Fractional dynamics and analysis of coupled Schrödinger-kdv equation with Caputo-Katugampola type memory

J Singh, A Gupta, D Baleanu - Journal of …, 2023 - asmedigitalcollection.asme.org
Fundamental purpose of the current research article is to analyze the behavior of obtained
results of time fractional nonlinear coupled Schrödinger-KdV equation, via implementing an …

Finite difference/collocation method for a generalized time-fractional KDV equation

W Cao, Y Xu, Z Zheng - Applied Sciences, 2018 - mdpi.com
In this paper, we studied the numerical solution of a time-fractional Korteweg–de Vries (KdV)
equation with new generalized fractional derivative proposed recently. The fractional …

The fractional analysis of a nonlinear mKdV equation with Caputo operator

HA Alyousef, R Shah, NA Shah, JD Chung… - Fractal and …, 2023 - mdpi.com
In this study, we aim to provide reliable methods for the initial value problem of the fractional
modified Korteweg–de Vries (mKdV) equations. Fractional differential equations are …

[PDF][PDF] A survey of KdV-CDG equations via nonsingular fractional operators

I Ullah, A Ullah, S Ahmad, H Ahmad, TA Nofal - AIMS Math, 2023 - researchgate.net
In this article, the Korteweg-de Vries-Caudrey-Dodd-Gibbon (KdV-CDG) equation is
explored via a fractional operator. A nonlocal differential operator with a nonsingular kernel …

[HTML][HTML] Study of fractional forced KdV equation with Caputo–Fabrizio and Atangana–Baleanu–Caputo differential operators

MM AlBaidani, F Aljuaydi, NS Alharthi, A Khan… - AIP Advances, 2024 - pubs.aip.org
It is essential for mathematicians, physicists, and engineers to construct fractional
mathematical models for specific phenomena and develop numerical or analytical solutions …

Comparison of Caputo and conformable derivatives for time-fractional Korteweg–de Vries equation via the finite difference method

A Yokuş - International Journal of Modern Physics B, 2018 - World Scientific
In this study, we investigate the nonlinear time-fractional Korteweg–de Vries (KdV) equation
by using the (1/G′)-expansion method and the finite forward difference method. We first …

[HTML][HTML] Investigation of fractal fractional nonlinear Drinfeld–Sokolov–Wilson system with non-singular operators

S Saifullah, A Ali, K Shah, C Promsakon - Results in Physics, 2022 - Elsevier
The aim of this article is to study the Drinfeld–Sokolov–Wilson equation considered in fractal-
fractional sense with exponential decay and Mittag-Leffler type kernels. The Laplace …