On the numerical solution of fractional parabolic partial differential equations with the Dirichlet condition

DOI10.1155/2012/696179zbMath1248.65085OpenAlexW2061839347WikidataQ58700711 ScholiaQ58700711MaRDI QIDQ714278

Zafer Cakir, Allaberen Ashyralyev

Publication date: 19 October 2012

Published in: Discrete Dynamics in Nature and Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/696179

zbMATH Keywords

stable difference schemesfractional parabolic equation

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Parabolic equations and parabolic systems (35K99) Fractional partial differential equations (35R11)

Related Items (13)

A high-accuracy MOC/FD method for solving fractional advection-diffusion equations ⋮ A novel equivalent definition of Caputo fractional derivative without singular kernel and superconvergent analysis ⋮ A two-grid block-centered finite difference method for the nonlinear time-fractional parabolic equation ⋮ FDM for fractional parabolic equations with the Neumann condition ⋮ Stability of difference schemes for fractional parabolic PDE with the Dirichlet-Neumann conditions ⋮ \(r\)-modified Crank-Nicolson difference scheme for fractional parabolic PDE ⋮ Uniqueness of an inverse problem for an integro-differential equation related to the Basset problem ⋮ A second-order finite difference scheme for quasilinear time fractional parabolic equation based on new fractional derivative ⋮ A Crank-Nicolson difference scheme for the time variable fractional mobile-immobile advection-dispersion equation ⋮ A note on the inverse problem for a fractional parabolic equation ⋮ A parallel CGS block-centered finite difference method for a nonlinear time-fractional parabolic equation ⋮ Solving the Caputo fractional reaction-diffusion equation on GPU ⋮ Well-Posedness and Approximation for Nonhomogeneous Fractional Differential Equations

Cites Work

• Two positive solutions for \((n - 1,1)\)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations
• Well-posedness of the Basset problem in spaces of smooth functions
• On the convergence of spline collocation methods for solving fractional differential equations
• Positivity and stability of the solutions of Caputo fractional linear time-invariant systems of any order with internal point delays
• Numerical solution for multi-term fractional (arbitrary) orders differential equations
• A note on the fractional hyperbolic differential and difference equations
• Weighted pseudo-almost periodic solutions of a class of semilinear fractional differential equations
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• A note on fractional derivatives and fractional powers of operators
• Numerical methods for multi-term fractional (arbitrary) orders differential equations
• Multi-order fractional differential equations and their numerical solution
• MULTIPLE POSITIVE SOLUTIONS FOR SEMIPOSITONE (n, p)-TYPE BOUNDARY VALUE PROBLEMS OF NONLINEAR FRACTIONAL DIFFERENTIAL EQUATIONS

This page was built for publication: On the numerical solution of fractional parabolic partial differential equations with the Dirichlet condition