An iterative approximation for time-fractional Cahn-Allen equation with reproducing kernel method

DOI10.1007/s40314-018-0672-9zbMath1413.35445OpenAlexW2811177600MaRDI QIDQ1715660

Onur Saldır, Mehmet Giyas Sakar, Fevzi Erdogan

Publication date: 29 January 2019

Published in: Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40314-018-0672-9

zbMATH Keywords

convergenceCaputo derivativereproducing kernel methodCahn-Allen equation

Mathematics Subject Classification ID

Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Fractional partial differential equations (35R11)

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Cites Work

• Unnamed Item
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• Iterative reproducing kernel Hilbert spaces method for Riccati differential equations
• Using reproducing kernel for solving a class of fractional partial differential equation with non-classical conditions
• Approximate solution of the fractional advection-dispersion equation
• Representation of exact solution for the time-fractional telegraph equation in the reproducing kernel space
• Fitted reproducing kernel Hilbert space method for the solutions of some certain classes of time-fractional partial differential equations subject to initial and Neumann boundary conditions
• The analysis of fractional differential equations. An application-oriented exposition using differential operators of Caputo type
• Travelling wave solutions of the Cahn-Allen equation by using first integral method
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• New approach for exact solutions of time fractional Cahn-Allen equation and time fractional phi-4 equation
• On solutions of fractional Riccati differential equations
• Enriched reproducing kernel particle method for fractional advection-diffusion equation
• Improving variational iteration method with auxiliary parameter for nonlinear time-fractional partial differential equations
• Traveling wave solutions for the hyperbolic Cahn-Allen equation
• A local reproducing kernel method accompanied by some different edge improvement techniques: application to the Burgers' equation
• Numerical solution of fractional Bratu type equations with Legendre reproducing kernel method
• A new approach for one-dimensional sine-Gordon equation
• Numerical solution of eighth-order boundary value problems in reproducing Kernel space
• An efficient computational intelligence approach for solving fractional order Riccati equations using ANN and SQP
• Design of unsupervised fractional neural network model optimized with interior point algorithm for solving Bagley-Torvik equation
• A Galerkin-reproducing kernel method: application to the 2D nonlinear coupled Burgers' equations
• Solving Fredholm integro-differential equations using reproducing kernel Hilbert space method
• Reproducing Kernel method for the solution of nonlinear hyperbolic telegraph equation with an integral condition
• Solving the reaction-diffusion equations with nonlocal boundary conditions based on reproducing kernel space
• A REPRODUCING KERNEL METHOD FOR SOLVING A CLASS OF NONLINEAR SYSTEMS OF PDES