Mathematics And Statistics - Research Publications

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    Symmetry reduction, conservation laws and power series solution of time-fractional variable coefficient Caudrey�Dodd�Gibbon�Sawada�Kotera equation
    (Springer Medizin, 2021-10-13T00:00:00) Manjeet; Gupta, Rajesh Kumar
    In this paper, Lie classical approach is utilized for the symmetry reduction of time-fractional variable coefficient Caudrey�Dodd�Gibbon�Sawada�Kotera equation. The obtained symmetries and Erde� lyi�Kober fractional differential operator are used to reduce the original nonlinear partial differential equation into nonlinear ordinary differential equation. The generalized Noether operator and new conservation theorem are exploited to obtain conservation laws of the governing equation. The power series solution is also derived for the considered equation. The obtained power series solution is investigated for the convergence and the obtained power series solution is convergent. � 2021, The Author(s), under exclusive licence to Islamic Azad University.
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    Invariance analysis, exact solution and conservation laws of (2 + 1) dim fractional kadomtsev-petviashvili (kp) system
    (MDPI AG, 2021-03-16T00:00:00) Kumar, Sachin; Kour, Baljinder; Yao, Shao-Wen; Inc, Mustafa; Osman, Mohamed S.
    In this work, a Lie group reduction for a (2 + 1) dimensional fractional Kadomtsev-Petviashvili (KP) system is determined by using the Lie symmetry method with Riemann Liouville derivative. After reducing the system into a two-dimensional nonlinear fractional partial differential system (NLFPDEs), the power series (PS) method is applied to obtain the exact solution. Further the obtained power series solution is analyzed for convergence. Then, using the new conservation theorem with a generalized Noether�s operator, the conservation laws of the KP system are obtained. � 2021 by the authors. Licensee MDPI, Basel, Switzerland.