Classical and nonclassical Lie symmetry analysis to a class of nonlinear time-fractional differential equations

Najafi, Ramin; Bahrami, Fariba; Hashemi, Mir Sajjad

doi:10.1007/s11071-016-3152-z

Cited by 40 publications

(9 citation statements)

References 43 publications

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“…Starting from a recent paper by Gazizov and Kasatkin [7], many papers have been devoted to the application of this method to find particular interesting classes of solutions also for fractional PDEs. We refer for example to the recent papers [10,13,15,17]. Indeed, there are few exact results regarding nonlinear fractional models that are motivated by different applications.…”

Section: The Invariant Subspace Methodsmentioning

confidence: 99%

Exact Results on Some Nonlinear Laguerre-Type Diffusion Equations

Garra

Tomovski

2021

Mathematical Modelling and Analysis

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In this paper we obtain some new explicit results for nonlinear equations involving Laguerre derivatives in space and/or in time. In particular, by using the invariant subspace method, we have many interesting cases admitting exact solutions in terms of Laguerre functions. Nonlinear diffusive-type and telegraph-type equations are considered and also the space and time-fractional counterpart are analyzed, involving Caputo or Prabhakar-type derivatives. The main aim of this paper is to point out that it is possible to construct many new interesting examples of nonlinear diffusive equations with variable coefficients admitting exact solutions in terms of Laguerre and Mittag-Leffler functions.

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Section: The Invariant Subspace Methodsmentioning

confidence: 99%

Exact Results on Some Nonlinear Laguerre-Type Diffusion Equations

Garra

Tomovski

2021

Mathematical Modelling and Analysis

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“…Here, some description for solving fractional partial differential equations (FPDEs) via Lie symmetry analysis will be provided. Surmise that FPDE having as in [16][17][18][19][20][21][22][23][24][25][26]]…”

Section: Lie Symmetry Analysis Of Fractional Partial Differential Equationsmentioning

confidence: 99%

Symmetry properties and exact solutions of the time fractional Kolmogorov-Petrovskii-Piskunov equation

Hashemi

Bayram

2019

Rev. Mex. Fís.

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“…Since the Lie symmetry analysis approach is mainly used to study integerorder NPDEs, it has an important theoretical research value to extend the method to NFPDEs. Although this method is not widely used in NFPDEs, there are still many achievements in this respect [60][61][62].…”

Section: Introductionmentioning

confidence: 99%

Time-fractional Davey–Stewartson equation: Lie point symmetries, similarity reductions, conservation laws and traveling wave solutions

Guo

Fang

Dong

2023

Commun. Theor. Phys.

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As a celebrated nonlinear water wave equation, the Davey-Stewartson equation is widely studied by researchers, especially in the field of mathematical physics. On the basis of Riemann-Liouville fractional derivative, the time fractional Davey-Stewartson equation is investigated in this paper. By application of the Lie symmetry analysis approach, the Lie point symmetries and symmetry groups are obtained. At the same time, the similarity reductions are derived. Furthermore, the equation is converted to a system of fractional partial differential equations and a system of fractional ordinary differential equations in the sense of Riemann-Liouville fractional derivative. By virtue of the symmetry corresponding to the scalar transformation, the equation is converted to a system of fractional ordinary differential equations in the sense of Erdélyi-Kober fractional integro-differential operators. By using Noether's theorem and Ibragimov's new conservation theorem, the conserved vectors and the conservation laws are derived. Finally, the traveling wave solutions are achieved and plotted.

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Classical and nonclassical Lie symmetry analysis to a class of nonlinear time-fractional differential equations

Cited by 40 publications

References 43 publications

Exact Results on Some Nonlinear Laguerre-Type Diffusion Equations

Exact Results on Some Nonlinear Laguerre-Type Diffusion Equations

Symmetry properties and exact solutions of the time fractional Kolmogorov-Petrovskii-Piskunov equation

Time-fractional Davey–Stewartson equation: Lie point symmetries, similarity reductions, conservation laws and traveling wave solutions

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