Group classification and symmetry reduction of three-dimensional nonlinear anomalous diffusion equation

DOI10.13108/2019-11-4-13zbMath1463.35497OpenAlexW3018433076MaRDI QIDQ5137847

A. A. Kasatkin, Rafail Kav'evich Gazizov, Stanislav Yu. Lukashchuk

Publication date: 2 December 2020

Published in: Ufimskii Matematicheskii Zhurnal (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/ufa488

zbMATH Keywords

fractional derivativessymmetry reductionoptimal system of subalgebrasnonlinear fractional diffusion equation

Mathematics Subject Classification ID

Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics (76M60) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (9)

Numerical schemes for integro-differential equations with Erdélyi-Kober fractional operator ⋮ Lie symmetry analysis and exact solutions of space-time fractional cubic Schrödinger equation ⋮ Lie symmetry analysis to general time-fractional Korteweg-de Vries equations ⋮ Lie group theory for nonlinear fractional \(K(m, n)\) type equation with variable coefficients ⋮ Group analysis of time-fractional equation with Riemann-Liouville derivative ⋮ Group classification and constructing conservation laws for time-fractional Sawada-Kotera-Parker-Dye equation ⋮ LIE SYMMETRY ANALYSIS TO THE WEAKLY COUPLED KAUP–KUPERSHMIDT EQUATION WITH TIME FRACTIONAL ORDER ⋮ SYMMETRY ANALYSIS, ANALYTICAL SOLUTIONS AND CONSERVATION LAWS OF A GENERALIZED KdV–BURGERS–KURAMOTO EQUATION AND ITS FRACTIONAL VERSION ⋮ GROUP ANALYSIS OF THE TIME FRACTIONAL (3 + 1)-DIMENSIONAL KDV-TYPE EQUATION

Cites Work

• Group classification of nonlinear time-fractional diffusion equation with a source term
• Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations
• Nonlinear porous medium flow with fractional potential pressure
• Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations
• Conservation laws of \((3+\alpha)\)-dimensional time-fractional diffusion equation
• Analytical studies of a time-fractional porous medium equation. Derivation, approximation and applications
• Subalgebras of real three- and four-dimensional Lie algebras
• CRC Handbook of Lie Group Analysis of Differential Equations, Volume I
• Symmetry reduction and invariant solutions for nonlinear fractional diffusion equation with a source term
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