Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 63Citation - Scopus: 71Lie Symmetry Analysis, Explicit Solutions and Conservation Laws for the Space-Time Fractional Nonlinear Evolution Equations(Elsevier, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, MustafaThis paper studies the symmetry analysis, explicit solutions, convergence analysis, and conservation laws (Cls) for two different space-time fractional nonlinear evolution equations with Riemann-Liouville (RL) derivative. The governing equations are reduced to nonlinear ordinary differential equation (ODE) of fractional order using their Lie point symmetries. In the reduced equations, the derivative is in Erdelyi-Kober (EK) sense, power series technique is applied to derive an explicit solutions for the reduced fractional ODEs. The convergence of the obtained power series solutions is also presented. Moreover, the new conservation theorem and the generalization of the Noether operators are developed to construct the nonlocal Cls for the equations. Some interesting figures for the obtained explicit solutions are presented. (C) 2018 Elsevier B.V. All rights reserved.Article Citation - WoS: 111Citation - Scopus: 113Lie Symmetry Analysis, Exact Solutions and Conservation Laws for the Time Fractional Caudrey-Dodd Equation(Elsevier, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, DumitruIn this work, we investigate the Lie symmetry analysis, exact solutions and conservation laws (Cls) to the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera (CDGDK) equation with Riemann-Liouville (RL) derivative. The time fractional CDGDK is reduced to nonlinear ordinary differential equation (ODE) of fractional order. New exact traveling wave solutions for the time fractional CDGDK are obtained by fractional sub-equation method. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. Ibragimov's nonlocal conservation method is applied to construct Cls for time fractional CDGDK. (C) 2017 Elsevier B.V. All rights reserved.Article Citation - WoS: 52Citation - Scopus: 50Optical Solitons, Nonlinear Self-Adjointness and Conservation Laws for Kundu-Eckhaus Equation(Elsevier Science Bv, 2017) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, DumitruIn this article, Kundu-Eckhaus equation (KE) is studied from the perspective of modified tanhcoth method (MTC), extended Jacobi elliptic function expansion method (EJEF), Lie symmetry analysis, nonlinear self-adjointness and conservation laws (Cls). New soliton solutions like combined dark-bright, dark, periodic wave and singular soliton solutions are obtained. The equation is found to be a nonlinear self-adjoint, we construct the Cls using the new conservation theorem presented by Ibragimov. Physical interpretation for some of the obtained solutions are illustrated in Figures.Article Citation - WoS: 40Citation - Scopus: 35Dark Optical Solitons and Conservation Laws To the Resonance Nonlinear Shrodinger's Equation With Kerr Law Nonlinearity(Elsevier Gmbh, 2017) Yusuf, Abdullahi; Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, DumitruIn this work, we investigate the soliton solutions to the resonant nonlinear Shrodinger's equation (R-NSE) with Kerr law nonlinearity. By adopting the Riccati-Bernoulli sub-ODE technique, we present the exact dark optical, dark-singular and periodic singular soliton solutions to the model. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. We studied the R-NSE by analyzing a system of nonlinear partial differential equations (NPDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system, then we apply the general conservation theorem to establish a set of nontrivial and nonlocal conservation laws (Cls). Some interesting figures for the acquired solutions are Cls also presented. (C) 2017 Elsevier GmbH. All rights reserved.