An investigation of a closed-form solution for non-linear variable-order fractional evolution equations via the fractional Caputo derivative

被引：6

作者：

Ali, Umair ^{[1
]}

Naeem, Muhammad ^{[2
]}

Alahmadi, Reham ^{[3
]}

Abdullah, Farah Aini ^{[4
]}

Khan, Muhammad Asim ^{[5
]}

Ganie, Abdul Hamid ^{[3
]}

机构：

[1] Inst Space Technol, Dept Appl Math & Stat, Islamabad, Pakistan

[2] Umm Al Qura Univ, Dept Math Appl Sci, Mecca, Saudi Arabia

[3] Saudi Elect Univ, Coll Sci & Theoret Studies, Dept Basic Sci, Riyadh, Saudi Arabia

[4] Univ Sains Malaysia, Sch Math Sci, George Town, Malaysia

[5] Univ Teknol Malaysia, Fac Sci, Dept Math Sci, Johor Baharu, Malaysia

来源：

FRONTIERS IN PHYSICS | 2023年 / 11卷

关键词：

space-time variable-order fractional shallow water wave equation; variable-order Caputo fractional derivative; Khater method; closed-form solution; graphical representation; PARTIAL-DIFFERENTIAL-EQUATIONS;

D O I：

10.3389/fphy.2023.1114319

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Determining the non-linear traveling or soliton wave solutions for variable-order fractional evolution equations (VO-FEEs) is very challenging and important tasks in recent research fields. This study aims to discuss the non-linear space-time variable-order fractional shallow water wave equation that represents non-linear dispersive waves in the shallow water channel by using the Khater method in the Caputo fractional derivative (CFD) sense. The transformation equation can be used to get the non-linear integer-order ordinary differential equation (ODE) from the proposed equation. Also, new exact solutions as kink- and periodic-type solutions for non-linear space-time variable-order fractional shallow water wave equations were constructed. This confirms that the non-linear fractional variable-order evolution equations are natural and very attractive in mathematical physics.

引用

页数：9

共 41 条

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