Skip to content
Research Article Open access CC BY 3.0

Fractional Sub-Equation Method and its Applications to the Space–Time Fractional Differential Equations in Mathematical Physics

J. F. Alzaidy

Journal of Advances in Mathematics and Computer Science · pp. 153–163 · Published 13 Mar 2013

10.9734/BJMCS/2013/2908

Abstract

In the present paper, we construct the analytical solutions of some nonlinear evolution equations involving Jumarie’s modified Riemann–Liouville derivative in mathematical physics; namely the space–time fractional modified Benjamin-Bona-Mahony(mBBM) equation and the space–time fractional Zakharov-Kuznetsov-Benjamin-Bona-Mahony(ZKBBM) equation by using a simple method which is called the fractional sub-equation method. As a result, three types of exact analytical solutions are obtained. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear fractional PDEs arising in mathematical physics.

Fractional sub-equation method fractional differential equation modified Riemann–Liouville derivative mittag-leffler function analytical solutions `

Cited by 78

Fractional stochastic Schrödinger evolution system with complex potential and poisson jumps: Qualitative behavior and T-controllability

Varshini Sandrasekaran, Ravikumar Kasinathan, Ramkumar Kasinathan · Partial Differential Equations in Applied Mathematics · 2024

New exact solutions for some fractional order differential equations via improved sub-equation method

Berat Karaagac · Discrete and Continuous Dynamical Systems - S · 2019

Exact Solutions of the Space Time Fractional Symmetric Regularized Long Wave Equation Using Different Methods

Özkan Güner, Dursun Eser · Advances in Mathematical Physics · 2014

Adequate closed form wave solutions to the space–time fractional nonlinear equations in physical sciences

M. Nurul Islam, M. Munnu Miah, M. Anisur Rahman · Partial Differential Equations in Applied Mathematics · 2021

Construction of Functional Closed Form Wave Solutions to the ZKBBM Equation and the Schrödinger Equation

Onur Alp Ilhan, M. Nurul Islam, M. Ali Akbar · Iranian Journal of Science and Technology, Transactions of Mechanical Engineering · 2020

Optical solitons solution of resonance nonlinear Schrödinger type equation with Atangana's-conformable derivative using sub-equation method

H. Yépez-Martínez, J. F. Gómez-Aguilar · Waves in Random and Complex Media · 2019

Invariant analysis and conservation laws of (2+1) dimensional time-fractional ZK–BBM equation in gravity water waves

S. Saha Ray, S. Sahoo · Computers & Mathematics with Applications · 2018

Existence and Hyers–Ulam Stability Analysis of Nonlinear Multi-Term Ψ-Caputo Fractional Differential Equations Incorporating Infinite Delay

Yating Xiong, Abu Bakr Elbukhari, Qixiang Dong · Fractal and Fractional · 2025

Multiple-order breathers for a generalized (3+1)-dimensional Kadomtsev–Petviashvili Benjamin–Bona–Mahony equation near the offshore structure

Yingying Xie, Lingfei Li · Mathematics and Computers in Simulation · 2022

Various Exact Solutions for the Conformable Time-Fractional Generalized Fitzhugh–Nagumo Equation with Time-Dependent Coefficients

Sami Injrou, Ramez Karroum, Nadia Deeb · International Journal of Differential Equations · 2021

Showing 20 of 78 known citations — external sources report more than can currently be individually listed.

Related research

Article metrics

Real usage data collected on this platform.

1

Page views

0

PDF downloads

0

Outbound clicks

78

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.