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Reductions and conservation laws for BBM and modified BBM equations

100%
Khorshidi M., Nadjafikhah M., Jafari H., Al Qurashi M.
Open Mathematics
|
2016
|
tom 14
|
nr 1
1138-1148
EN
In this paper, the classical Lie theory is applied to study the Benjamin-Bona-Mahony (BBM) and modified Benjamin-Bona-Mahony equations (MBBM) to obtain their symmetries, invariant solutions, symmetry reductions and differential invariants. By observation of the the adjoint representation of Mentioned symmetry groups on their Lie algebras, we find the primary classification (optimal system) of their group-invariant solutions which provides new exact solutions to BBM and MBBM equations. Finally, conservation laws of the BBM and MBBM equations are presented. Some aspects of their symmetry properties are given too.
2
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Fractional derivative generalization of Noether’s theorem

100%
Khorshidi M., Nadjafikhah M., Jafari H.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
The symmetry of the Bagley–Torvik equation is investigated by using the Lie group analysis method. The Bagley–Torvik equation in the sense of the Riemann–Liouville derivatives is considered. Then we prove a Noetherlike theorem for fractional Lagrangian densities with the Riemann-Liouville fractional derivative and few examples are presented as an application of the theory.
3
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Results for Mild solution of fractional coupled hybrid boundary value problems

100%
Baleanu D., Jafari H., Khan H., Johnston S. J.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
The study of coupled system of hybrid fractional differential equations (HFDEs) needs the attention of scientists for the exploration of its different important aspects. Our aim in this paper is to study the existence and uniqueness of mild solution (EUMS) of a coupled system of HFDEs. The novelty of this work is the study of a coupled system of fractional order hybrid boundary value problems (HBVP) with n initial and boundary hybrid conditions. For this purpose, we are utilizing some classical results, Leray–Schauder Alternative (LSA) and Banach Contraction Principle (BCP). Some examples are given for the illustration of applications of our results.
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