Skip to content
Research Article Open access CC BY 3.0

Fractional Sub-equation Method and Analytical Solutions to the Hirota-satsuma Coupled KdV Equation and Coupled mKdV Equation

H. Yépez-Martínez, J. M. Reyes, I. O. Sosa

Journal of Advances in Mathematics and Computer Science · pp. 572–589 · Published 21 Nov 2013

10.9734/BJMCS/2014/7059

Abstract

The fractional sub-equation method is proposed to construct analytical solutions of nonlinear fractional partial differential equations (FPDEs), involving Jumarie’s modified Riemann-Liouville derivative. The fractional sub-equation method is applied to the space-time fractional generalized Hirota-Satsuma coupled KdV equation and coupled mKdV equation. The analytical solutions show that the fractional sub-equation method is very effective for the fractional coupled KdV and mKdV equations. The solutions are compared with that of the extended tanh-function method. New exact solutions are found for the coupled mKdV equation.

Fractional sub-equation method Analytical solutions Nonlinear KdV and mKdV fractional equations.

Cited by 18

Q-homotopy analysis method for time-fractional Newell–Whitehead equation and time-fractional generalized Hirota–Satsuma coupled KdV system

Di Liu, Qiongya Gu, Lizhen Wang · Communications in Theoretical Physics · 2024

On the soliton solutions to the density-dependent space time fractional reaction–diffusion equation with conformable and M-truncated derivatives

Handenur Esen, N. Ozdemir, A. Seçer · Optical and quantum electronics · 2023

Two efficient computational technique for fractional nonlinear Hirota–Satsuma coupled KdV equations

A. Prakash, Vijay Verma · 2020

Exact traveling wave solutions of density-dependent conformable space–time-fractional diffusion–reaction equation with quadratic nonlinearity

H. Rezazadeh, Alper Korkmaz, H. Yépez-Martínez · Indian Journal of Physics · 2019

Study on Fractional Differential Equations with Modified Riemann–Liouville Derivative via Kudryashov Method

E. Aksoy, A. Bekir, A. Cevikel · International journal of nonlinear sciences and numerical simulation · 2019

Closed form solutions to the coupled space-time fractional evolution equations in mathematical physics through analytical method

M. N. Islam, M. Akbar · JOURNAL OF MECHANICS OF CONTINUA AND MATHEMATICAL SCIENCES · 2018

Lie symmetry analysis, conservation laws and exact solutions of the time-fractional generalized Hirota–Satsuma coupled KdV system

Elaheh Saberi, S. Hejazi · 2018

Series Solution for the Time-Fractional Coupled mKdV Equation Using the Homotopy Analysis Method

J. Gómez-Aguilar, H. Yépez-Martínez, R. Escobar-Jiménez · 2016

Fractional Subequation Method

· Computational Fractional Dynamical Systems · 2022

Closed form soliton solutions to the space-time fractional foam drainage equation and coupled mKdV evolution equations

Onur Alp İlhan, Fatma Berna Benli, M. Nurul Islam · International Journal of Nonlinear Sciences and Numerical Simulation · 2021

Showing 10 of 18 known citations — external sources report more than can currently be individually listed.

Related research

Article metrics

Real usage data collected on this platform.

14

Page views

0

PDF downloads

0

Outbound clicks

18

Citations

Views over time

Views by country

Approximate, from request IP at view time — not citizenship or institution. Countries with fewer than 5 views are grouped as "Other".

Traffic sources

Referring site, by host.

Views and downloads exclude known bots/crawlers. Citations combines this platform's own DOI-resolved index with each external source's own reported total — see Cited by above for individually listed citing works. Last refreshed 0 seconds ago.