Symmetry analysis and conservation laws to the space-fractional Prandtl equation

DOI10.1007/s11071-017-3730-8zbMath1390.37113OpenAlexW2746544483MaRDI QIDQ1637270

Mingyang Pan, Lian-Cun Zheng, Chun Yan Liu, Fawang Liu

Publication date: 7 June 2018

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-017-3730-8

zbMATH Keywords

conservation lawsLie groupsimilarity solutionPrandtl equation

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10)

Related Items (5)

Group classifications, optimal systems, symmetry reductions and conservation law of the generalized fractional porous medium equation ⋮ Group classification, symmetry reductions and exact solutions of the time-fractional generalized thin film equation with variable coefficients ⋮ Symmetries, explicit solutions and conservation laws for some time space fractional nonlinear systems ⋮ Exact and numerical solutions of time-fractional advection-diffusion equation with a nonlinear source term by means of the Lie symmetries ⋮ An approximate similarity solution for spatial fractional boundary-layer flow over an infinite vertical plate

Uses Software

• FracSym

Cites Work

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• Group classification of nonlinear time-fractional diffusion equation with a source term
• FracSym: automated symbolic computation of Lie symmetries of fractional differential equations
• Symmetry analysis and conservation laws for the class of time-fractional nonlinear dispersive equation
• Fractional Lie group method of the time-fractional Boussinesq equation
• A partial Lagrangian method for dynamical systems
• Nonlocal symmetry analysis and conservation laws to an third-order Burgers equation
• Piecewise polynomial collocation for linear boundary value problems of fractional differential equations
• Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations
• Existence and multiplicity of positive solutions for singular fractional boundary value problems
• A foundational approach to the Lie theory for fractional order partial differential equations
• Nonlinear self-adjointness, conservation laws and exact solutions of time-fractional Kompaneets equations
• Invariant analysis of nonlinear fractional ordinary differential equations with Riemann-Liouville fractional derivative
• Conservation laws for time-fractional subdiffusion and diffusion-wave equations
• A new conservation theorem
• Constructing conservation laws for fractional-order integro-differential equations
• On the fractional Adams method
• Conservation laws and conserved quantities for laminar two-dimensional and radial jets
• Applications of symmetry methods to partial differential equations
• Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations
• Symmetry and integration methods for differential equations
• Detailed error analysis for a fractional Adams method
• Formulation of Euler-Lagrange equations for fractional variational problems
• Lie group analysis and similarity solution for fractional Blasius flow
• Lie symmetries and conservation laws for the time fractional Derrida-Lebowitz-Speer-Spohn equation
• Numerical methods for solving the multi-term time-fractional wave-diffusion equation
• Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics
• A theorem on the existence of symmetries of fractional PDEs
• Comparison of numerical methods for fractional differential equations
• On the construction of conservation laws: A mixed approach
• Nonlinear self-adjointness and conservation laws
• Similarity solutions of the two-dimensional unsteady boundary-layer equations
• Mechanics with variable-order differential operators
• Direct Construction of Conservation Laws from Field Equations
• Unsteady separated stagnation-point flow of an incompressible viscous fluid on the surface of a moving porous plate
• Initial conditions-independent limit cycles of a fractional-order van der Pol oscillator
• Fractional variational calculus and the transversality conditions
• The boundary layer on a magnetized plate

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