Lie symmetry, convergence analysis, explicit solutions, and conservation laws for the time-fractional modified Benjamin-Bona-Mahony equation

• Autorzy: Al-deiakeh Rawaya , Alquran Marwan , Ali Mohammed , Qureshi Sania , Momani Shaher , Malkawi Abed Al-Rahman

Identyfikatory

DOI

10.17512/jamcm.2024.1.02

• Języki publikacji: EN

Abstrakty

EN

Lie symmetry analysis is considercd as one of the most powerful techniques that has been used for analyzing and extracting various types of solulions to partial differential equations. Conservation laws reflect important aspects of the behavior and pcoperties of physical systems. This paper focuses on the investigation of the (1+1)-dimensional time-fractional modified Benjamin-Bona-Mahony equation (mBBM) incorporating Riemann-Louville derivatives (RLD). Through the application of Lie symmetry analysis, ihe study cxplores similarity reductions and transforms the problem into a nonlinear ordinary differential equation with fractional order. A power series solution is obtained using the Erdelyi-Kober fractional operator, and the convergence of the solutions is analyzed. Furthemore, novel conservation laws for the time-fractional mBBM equation are established. The findings of the current work contribute to a deeper understanding of the dynamics of this fractional evolution equation and provide valuable insights into its behavior.

Słowa kluczowe

EN

modified Benjamin-Bona-Mahony equation; fractional partial differential equation; Lie symmetry; Riemann-Liouville derivative

PL

ułamkowe równanie różniczkowe cząstkowe; symetria; pochodna ułamkowa Riemanna Liouville'a

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2024
• Tom: Vol. 23, nr 1
• Strony: 19--31
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Al-deiakeh Rawaya

• Nonlinear Dynamics Research Cenier (NDRC), Ajman University Ajman, UAE
• Department of Mathematics, Irbid National University Irbid 2110 Jordan

autor

Alquran Marwan

• Department of Mathematics and Statistics, Jordan University of Science & Technology Irbid 22110, Jordan

autor

Ali Mohammed

• Department of Mathematics and Statistics, Jordan University of Science & Technology Irbid 22110, Jordan

autor

Qureshi Sania

• Department of Basics Sciences and Related Studies Mehran University of Engineering and Technology, Jamshoro 76062 Pakistan
• Department of Mathematics Near Est University Mersin 99138 Turkey
• Department of Computer Science and Mthematics Lebanese American University Beirut, Lebanon

autor

Momani Shaher

• Nonlinear Dynamics Research Cenier (NDRC), Ajman University Ajman, UAE
• Department of Mathematics The University of Jordan Amman, Jordan

autor

Malkawi Abed Al-Rahman

• Department of Mathematics The University of Jordan Amman, Jordan

Bibliografia

• [1] Podlubny, 1. (1999). Fractional Differrential Equations. Academic Press.
• [2] Mainardi, F, (2010), Frational Calculus and Waves in Linear Viscoelascity. Imperial College Press.
• [3] Rawashdeh. E,A. (2006). Numerical solution of fractional integro-differential equations by collocation method. Applied Muthematics and Computation 176 (1) 1-6.
• [4] Bhrawy, A.H., Alzaidy, J.F., Abdelkawy, M,A., &Biswas, A. (2016). Jacobi spectral collocation approximation for multi-dimensional time-fractional Schrodinger equations. Nonlinear Dynamics, 84(3). 1553-1567.
• [5] Abu Arqub, O., Al-Smadi. M., Abu Gdairi, R., Alhodaly. M , & Hayat, T. (2021). Implementation of reproducing kernel Hilbert algorithm for point wise numerical, solvability of fractional Burgers' model in time-dependent variable domain regarding constraint boundary condition of Robin ResuIts in Physics,24, 104210,
• [6] Alquran, M (2023). The amazing fraclional Maclaurin series for solving different types of fraclional mathematical problems that arise in physics and engineering. Partial Differential Equations in Applied Mathematics, 7. 100506.
• [7] Alquran, M. (2023). lnvestigating the revisited generalized stochastic potential-KdV equation; Fractional time-derivative against proponional time-delay. Romanian Journal of Physics, 68(.t-4). 106.
• [8] Jaradat. 1., Alquran. M., Momani, S., &. Baleanu, D. (2020). Numerical schemes for studying biomathematics model inherited with memory-time and delay-time, Alexandra Engineering Journal. 59(5), 2969-2974,
• [9] Alquran. M., Ali. M., Alsukhour, M., & Jaradat, I. (2020). Promoted residual power series technique with Laplace transform to solve some time-fractional problems arising in physics. Results in Physics, 19, 103667.
• [10] Alquran, M.. Alsukhour, M., Ali. M.. & Jaradal. I. (2021). Combination of Laplace transform and residual power series techniques to solve autonomous n-dimensional fractional nonlinear systems. Nonlinear Engineering, 10(1), 282-292,
• [11] Kumar, K., Nisar, K,S.. & Niwas. M. (2023). On the dynamics of exacts solutions to a (3+1 )-dimensional YTSF equation emerging in shallow sea waves: Lie symmetry analysis and generalized Kudryashov method. Results in Physics, 48, 106432.
• [12] Kumar, K., Nisar., K.S., & Kumar, A. (2021). A (2+1)-dimensionaI gereralized Hirota-Satsuma-Ito equations: Lie symmetry analysis. invariant solutions and dynamics of solution soIutions. Results in Physics 28, 104621.
• [13] Jhangeer, A„ Hussain, A., Junaid-U-Rehman. M., Khan, I., Baleanu, D,, & Nisar, K.S. (2020). Lie analysis, conservation laws and travelling wave structures of nonlinear Bogoyavlenskii-Kadomtsev-Petviashvili equation. Results in Physics, 19, 103492.
• [14] Hussain, A. Bano, S. Khan, I., Baleanu, D., & Nisar, K.S. (2020), Lie symmetry analysis, esplicit solutions and conservation laws of a spatially two-dimensional Burgers-Huxley equation. Symmetry. 12, 170.
• [15] Al-Deiakeh, R., Alquran, M., Ali. M., Yusuf, A., & Momani, S. (2022). On group of Lie symmetry analysis, explicit solutions and conservation laws ot the time-fractional (2+1 )-dimensional Zakharov-Kuznetsov (q,p,r) equation. Journal of Geometry and Physics. 174(1), 104512.
• [16] Ibragimov, N.H. (2007). A new conservation theorem. Journal of Mathematical Analysis and Application, 28. 311-333.
• [17] Shakeel. M., Manan. A., Bin Turki. N., Shah, N.A., & Tag, S.M. (2023). Novel analytical technique to find diversity of solitary wave solutions for Wazwaz-Benjamin-Bona Mahony equations of fractional order. Results in Physics, 51. 106671.
• [18] Shakeel, M., Attaullah, Bin Turki, N., Shah. N.A., & Tag, S.M. (2023). Diversity of soliton Solutions in the (3+1)-dimensional Wazwaz-Benjaiuin-Bona-Mahony equations arising in mathematical physics. Results in Physics, 51, 106624,
• [19] Shakeel, M. Altaullah, El-Zahar, E.R., Shah. N.A.. & Chung. J.D. (2022). Generalized exp-funcion method to find closed form solutions of nonlinear disperive modified Benjamin--Bona-Mahony equation defined hy seismic sea waves. Mathematics, 10, 1026.
• [20] Wang. G.W., Liu, X.Q., & Zhang, Y.Y. (2013). Lie symmetry analysis to the time frattional generalized fifht-order KdV equation. Comminications in Nonlinear Science and Numerical Simulalion, 18, 2321-2326.
• [21] Atangana, A., Baleanu, D., & Alsaedi, A. (2015). New properties of conformable derivative. Open Mathematics, I3(1). 1-10.
• [22] Olver, P.J. (1993). Applications of Lie Groups to Differential Equatios Springer.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).