Regularity of Solutions to a Time-Fractional Diffusion Equation
نویسنده
چکیده
The paper proves estimates for the partial derivatives of the solution to a time-fractional diffusion equation, posed over a bounded spatial domain. Such estimates are needed for the analysis of effective numerical methods, particularly since the solution is less regular than in the well-known case of classical diffusion.
منابع مشابه
A Parabolic Problem with a Fractional Time Derivative
We study regularity for a parabolic problem with fractional diffusion in space and a fractional time derivative. Our main result is a De Giorgi-Nash-Moser Hölder regularity theorem for solutions in a divergence form equation. We also prove results regarding existence, uniqueness, and higher regularity in time.
متن کاملA numerical method for solving a class of distributed order time-fractional diffusion partial differential equations according to Caputo-Prabhakar fractional derivative
In this paper, a time-fractional diffusion equation of distributed order including the Caputo-Prabhakar fractional derivative is studied. We use a numerical method based on the linear B-spline interpolation and finite difference method to study the solutions of these types of fractional equations. Finally, some numerical examples are presented for the performance and accuracy of the proposed nu...
متن کاملA New Implicit Finite Difference Method for Solving Time Fractional Diffusion Equation
In this paper, a time fractional diffusion equation on a finite domain is con- sidered. The time fractional diffusion equation is obtained from the standard diffusion equation by replacing the first order time derivative by a fractional derivative of order 0 < a< 1 (in the Riemann-Liovill or Caputo sence). In equation that we consider the time fractional derivative is in...
متن کاملFinite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients
In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integ...
متن کاملNonlinear Cable equation, Fractional differential equation, Radial point interpolation method, Meshless local Petrov – Galerkin, Stability analysis
The cable equation is one the most fundamental mathematical models in the neuroscience, which describes the electro-diffusion of ions in denderits. New findings indicate that the standard cable equation is inadequate for describing the process of electro-diffusion of ions. So, recently, the cable model has been modified based on the theory of fractional calculus. In this paper, the two dimensio...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010