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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Explicit Solutions of Coupled Time Fractional Kaup-Boussinesq Equation with Weak Dispersion

Journal of Applied Nonlinear Dynamics 8(4) (2019) 585--594 | DOI:10.5890/JAND.2019.12.006

Hemanta Mandal, B. Bira

Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur, Chennai-603203, India

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Abstract

In the current article, we consider a system of time fractional Kaup-Boussinesq shallow water equations. Using Lie group analysis, we obtain the symmetry group of transformations which reduces the system of fractional partial differential equations (FPDEs) to system of fractional ordinary differential equations (FODEs). Further, we investigate the exact explicit group invariant solution as well as power series solution of the given system of equations. Next the physical significance of the group invariant solution under the influence of fractional order is studied graphically. Lastly, conserved vectors for the FPDEs are obtained using the conservation theorem.

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