Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 104Citation - Scopus: 107Time-Fractional Cahn-Allen and Time-Fractional Klein-Gordon Equations: Lie Symmetry Analysis, Explicit Solutions and Convergence Analysis(Elsevier Science Bv, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa; Isa Aliyu, AliyuThis research analyzes the symmetry analysis, explicit solutions and convergence analysis to the time fractional Cahn-Allen (CA) and time-fractional Klein-Gordon (KG) equations with Riemann-Liouville (RL) derivative. The time fractional CA and time fractional KG are reduced to respective nonlinear ordinary differential equation of fractional order. We solve the reduced fractional ODEs using an explicit power series method. The convergence analysis for the obtained explicit solutions are investigated. Some figures for the obtained explicit solutions are also presented. (C) 2017 Elsevier B.V. All rights reserved.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: 51Citation - Scopus: 53New Solitary Wave Solutions and Conservation Laws To the Kudryashov-Sinelshchikov Equation(Elsevier Gmbh, Urban & Fischer verlag, 2017) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, MustafaIn this manuscript, we utilized the algorithm of Riccati Bernoulli sub-ODE method to find new soliton solutions to the Kudryashov Sinelshchikov equation (KSE). Some new type of traveling wave solutions are acquired, which includes the kink-type, singular-type and exponential function solutions which have not been obtained in previous time using this technique. The obtained solutions appear with all necessary constraint conditions that are necessary for them to exist. Using the general conservation laws (Cls) theorem introduced by Ibragimov, the Cls for the underlying equation are investigated. (C) 2017 Elsevier GmbH. All rights reserved.Article Citation - WoS: 34Citation - Scopus: 39Lie Symmetry Analysis and Conservation Laws for the Time Fractional Simplified Modified Kawahara Equation(Sciendo, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, DumitruIn this work, Lie symmetry analysis for the time fractional simplified modified Kawahara (SMK) equation with Riemann-Liouville (RL) derivative, is analyzed. We transform the time fractional SMK equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable. In the reduced equation, the derivative is in the Erdelyi-Kober (EK) sense. We solve the reduced fractional ODE using a power series technique. Using Ibragimov's nonlocal conservation method to time fractional partial differential equations, we compute conservation laws (Cls) for the time fractional SMK equation. Some figures of the obtained explicit solution are presented.Article Citation - WoS: 56Citation - Scopus: 57Lie Symmetry Analysis, Exact Solutions and Conservation Laws for the Time Fractional Modified Zakharov-Kuznetsov Equation(inst Mathematics & informatics, 2017) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, DumitruIn this work, Lie symmetry analysis (LSA) for the time fractional modified Zakharov-Kuznetsov (mZK) equation with Riemann-Liouville (RL) derivative is analyzed. We transform the time fractional mZK equation to nonlinear ordinary differential equation (ODE) of fractional order using its point symmetries with a new dependent variable. In the reduced equation, the derivative is in Erdelyi-Kober (EK) sense. We obtained exact traveling wave solutions by using fractional D(xi)(alpha)G/G-expansion method. Using Ibragimov's nonlocal conservation method to time fractional nonlinear partial differential equations (FNPDEs), we compute conservation laws (CLs) for the mZK equation.