Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 Journal of Applied Mathematics and Computational Mechanics

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: pochodna ułamkowa Riemanna Liouville'a

Sortuj według:

Ogranicz wyniki do:

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

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

Journal of Applied Mathematics and Computational Mechanics

2024

Vol. 23, nr 1

19-31

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.

Group invariant solution of some time fractional evolution equations

Mandal H., Bira B.

Journal of Applied Mathematics and Computational Mechanics

2018

Vol. 17, nr 4

35--46

In this paper, we consider some classes of a system of nonlinear fractional differential equations (FDEs) arising in some important physical phenomena. Using symmetry group of transformations, the given systems of fractional partial differential equations (FPDEs) are reduced to systems of fractional ordinary differential equations (FODEs). Further, using the group invariant condition, we solve the reduced systems of FODEs and exact solutions of the given equations are constructed. Finally, the physical significance of the solutions are investigated graphically based on the exact solutions in order to highlight the importance of the study.