Group-Invariant Solutions of Fractional Differential Equations

Газизов, Р. К.; Kasatkin, Alexey A.; Lukashchuk, Stanislav Yu.

doi:10.1007/978-90-481-9884-9_5

Cited by 36 publications

(35 citation statements)

References 3 publications

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“…FDEs have been studied nowadays to describe several physical aspects and procedure in natural conditions [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. However, fractional partial differential equations (FPDEs) having only time derivative have been analyzed via the Lie symmetry method [20][21][22][23][24][25][26]. Recently, the Lie method has been developed to the systems of time FPDEs [27].…”

Section: Introductionmentioning

confidence: 99%

Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws

2018

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This article uses the extension of the Lie symmetry analysis (LSA) and conservation laws (Cls) (Singla et al. in Nonlinear Dyn. 89(1):321-331, 2017; Singla et al. in J. Math. Phys. 58:051503, 2017) for the space-time fractional partial differential equations (STFPDEs) to analyze the space-time fractional Rosenou-Haynam equation (STFRHE) with Riemann-Liouville (RL) derivative. We transform the space-time fractional RHE to a nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries. The reduced equation's derivative is in Erdelyi-Kober (EK) sense. We use the power series (PS) technique to derive explicit solutions for the reduced ODE for the first time. The Cls for the governing equation are constructed using a new conservation theorem.

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Section: Introductionmentioning

confidence: 99%

Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws

2018

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“…It was not common to apply the symmetry properties for studying fractional differential equations. In [10], Gazizov et al used Lie continuous groups for symmetry analysis of the fractional differential equations and suggested a formula for fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

Lie group method and fractional differential equations

Zedan¹,

Abu-Nawas²

2017

J. Nonlinear Sci. Appl.

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“…Some books and studies that we can use as the basis for fractional-order differential equations are [6,17,18,25,26,29,31]. Let us consider the differential equation with fractional derivative of order α.…”

Section: Basic Concept and Definitions For Fractional-order Differentmentioning

confidence: 99%

“…Prolongation formula can be easily generalized for fractional equations of order α [17,18,21,25,28],…”

Section: Basic Concept and Definitions For Fractional-order Differentmentioning

confidence: 99%

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Lie symmetry analysis of the Hanta-epidemic systems

Ongun¹,

Kocabiyik²

2017

J. Math. Computer Sci.

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We consider a model for the fatal Hanta-virus infection among mice. Lie symmetry analysis is applied to find general solutions to Hanta-virus model, which is also known as Abramson-Kenkre model. Besides the solution for the version with derivatives of fractional order, we investigate the model also by using the Lie symmetry method. The basic point of view for both situations will be logistic differential equation, created for total population.

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Group-Invariant Solutions of Fractional Differential Equations

Cited by 36 publications

References 3 publications

Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws

Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws

Lie group method and fractional differential equations

Lie symmetry analysis of the Hanta-epidemic systems

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