Conservation laws of \((3+\alpha)\)-dimensional time-fractional diffusion equation

DOI10.1016/J.CAMWA.2017.10.001zbMath1408.37132OpenAlexW2765684866WikidataQ114851930 ScholiaQ114851930MaRDI QIDQ1732358

Elham Lashkarian, Elham Dastranj, S. Reza Hejazi

Publication date: 25 March 2019

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2017.10.001

zbMATH Keywords

Laplace operatorfractional diffusion equationfractional conservation lawsNoether's operatorfractional symmetry

Mathematics Subject Classification ID

Geometric theory, characteristics, transformations in context of PDEs (35A30) Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems (37L50) Symmetries of infinite-dimensional dissipative dynamical systems (37L20) Fractional partial differential equations (35R11)

Related Items (11)

Lie symmetry analysis, conservation laws and numerical approximations of time-fractional Fokker-Planck equations for special stochastic process in foreign exchange markets ⋮ Anisotropic non-linear time-fractional diffusion equation with a source term: classification via Lie point symmetries, analytic solutions and numerical simulation ⋮ Group formalism of Lie transformations, conservation laws, exact and numerical solutions of non-linear time-fractional Black-Scholes equation ⋮ Group analysis, invariance results, exact solutions and conservation laws of the perturbed fractional Boussinesq equation ⋮ Lie group analysis and conservation laws for the time-fractional third order KdV-type equation with a small perturbation parameter ⋮ Invariant analysis, conservation laws, and some exact solutions for \((2+1)\)-dimension fractional long-wave dispersive system ⋮ Group classification and symmetry reduction of three-dimensional nonlinear anomalous diffusion equation ⋮ Symmetry classification and exact solutions of (3 + 1)-dimensional fractional nonlinear incompressible non-hydrostatic coupled Boussinesq equations ⋮ \(\alpha\)-robust \(H^1\)-norm convergence analysis of ADI scheme for two-dimensional time-fractional diffusion equation ⋮ Unnamed Item ⋮ Numerical conservation laws of time fractional diffusion PDEs

Cites Work

• Unnamed Item
• Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations
• Nonlinear self-adjointness, conservation laws and exact solutions of time-fractional Kompaneets equations
• Conservation laws for time-fractional subdiffusion and diffusion-wave equations
• A new conservation theorem
• The fractional calculus. Theory and applications of differentiation and integration to arbitrary order
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• Symmetry and integration methods for differential equations
• Lie symmetry analysis to the time fractional generalized fifth-order KdV equation
• Invariant analysis and exact solutions of nonlinear time fractional Sharma-Tasso-Olver equation by Lie group analysis
• Complete Group Classifications and Symmetry Reductions of the Fractional Fifth-Order KdV Types of Equations
• Comparing symmetries and conservation laws of nonlinear telegraph equations
• Direct Construction of Conservation Laws from Field Equations
• Direct construction method for conservation laws of partial differential equations Part II: General treatment

This page was built for publication: Conservation laws of \((3+\alpha)\)-dimensional time-fractional diffusion equation