Analysis of Kink Behaviour of KdV-mKdV Equation under Caputo Fractional Operator with Non-Singular Kernel

被引：5
|
作者：
Ali, Sajjad [1 ]
Ullah, Aman [1 ]
Ahmad, Shabir [1 ]
Nonlaopon, Kamsing [2 ]
Akgul, Ali [3 ,4 ]
机构：
[1] Univ Malakand, Dept Math, Chakdara 18800, Khyber Pakhtunk, Pakistan
[2] Khon Kaen Univ, Fac Sci, Dept Math, Khon Kaen 40002, Thailand
[3] Siirt Univ, Art & Sci Fac, Dept Math, TR-56100 Siirt, Turkey
[4] Near East Univ, Math Res Ctr, Dept Math, Near East Blvd, TR-99138 Nicosia, Turkey
来源：
SYMMETRY-BASEL | 2022年 / 14卷 / 11期
关键词：
modified KdV equation; kink solution; Caputo operator; stability; SOLITARY WAVES;
D O I：
10.3390/sym14112316
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The KdV equation has many applications in mechanics and wave dynamics. Therefore, researchers are carrying out work to develop and analyze modified and generalized forms of the standard KdV equation. In this paper, we inspect the KdV-mKdV equation, which is a modified and generalized form of the ordinary KdV equation. We use the fractional operator in the Caputo sense to analyze the equation. We examine some theoretical results concerned with the solution's existence, uniqueness, and stability. We employ a modified Laplace method to extract the numerical results of the considered equation. We use MATLAB-2020 to simulate the results in a few fractional orders. We report the effects of the fractional order on the wave dynamics of the proposed equation.
引用
收藏
页数：17
相关论文
共 50 条
  • [1] Fractional view analysis of Kersten-Krasil?shchik coupled KdV-mKdV systems with non-singular kernel derivatives
    Al-Sawalha, M. Mossa
    Shah, Rasool
    Khan, Adnan
    Ababneh, Osama Y.
    Botmart, Thongchai
    AIMS MATHEMATICS, 2022, 7 (10): : 18334 - 18359
  • [2] A survey of (2+1)-dimensional KdV-mKdV equation using nonlocal Caputo fractal-fractional operator
    Jamal, Abdul
    Ullah, Aman
    Ahmad, Shabir
    Sarwar, Shahzad
    Shokri, Ali
    RESULTS IN PHYSICS, 2023, 46
  • [3] The Fractional Analysis of a Nonlinear mKdV Equation with Caputo Operator
    Alyousef, Haifa A.
    Shah, Rasool
    Shah, Nehad Ali
    Chung, Jae Dong
    Ismaeel, Sherif M. E.
    El-Tantawy, Samir A.
    FRACTAL AND FRACTIONAL, 2023, 7 (03)
  • [4] Fractional Diffusion Equation under Singular and Non-Singular Kernel and Its Stability
    Gabrick, Enrique C.
    Protachevicz, Paulo R.
    Lenzi, Ervin K.
    Sayari, Elaheh
    Trobia, Jose
    Lenzi, Marcelo K.
    Borges, Fernando S.
    Caldas, Ibere L.
    Batista, Antonio M.
    FRACTAL AND FRACTIONAL, 2023, 7 (11)
  • [5] ANALYSIS OF THE TRANSMISSION OF NIPAH VIRUS UNDER FRACTIONAL OPERATOR WITH NON-SINGULAR AND NONLOCAL KERNEL
    Ali, Arshad
    Yousef, Ali
    Ullah, Aman
    Ahmad, Shabir
    Naz, Hafsa
    Al-Mdallal, Qasem M.
    FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2022, 30 (10)
  • [6] Analysis of the cable equation with non-local and non-singular kernel fractional derivative
    Berat Karaagac
    The European Physical Journal Plus, 133
  • [7] Analysis of logistic equation pertaining to a new fractional derivative with non-singular kernel
    Kumar, Devendra
    Singh, Jagdev
    Al Qurashi, Maysaa
    Baleanu, Dumitru
    ADVANCES IN MECHANICAL ENGINEERING, 2017, 9 (02):
  • [8] Analysis of the cable equation with non-local and non-singular kernel fractional derivative
    Karaagac, Berat
    EUROPEAN PHYSICAL JOURNAL PLUS, 2018, 133 (02):
  • [9] Schrodinger equation involving fractional operators with non-singular kernel
    Gomez-Aguilar, J. F.
    Baleanu, Dumitru
    JOURNAL OF ELECTROMAGNETIC WAVES AND APPLICATIONS, 2017, 31 (07) : 752 - 761
  • [10] Comparative qualitative analysis and numerical solution of conformable fractional derivative generalized KdV-mKdV equation
    Kumar, Rajeev
    Dharra, Rahul
    Kumar, Sanjeev
    INTERNATIONAL JOURNAL OF SYSTEM ASSURANCE ENGINEERING AND MANAGEMENT, 2023, 14 (04) : 1247 - 1254
12345