Displaying similar documents to “A finite difference approach for the initial-boundary value problem of the fractional Klein-Kramers equation in phase space”

A finite difference method for fractional diffusion equations with Neumann boundary conditions

Béla J. Szekeres, Ferenc Izsák (2015)

Open Mathematics

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A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. The basis of the mathematical model and the numerical approximation is an appropriate extension of the initial values, which incorporates homogeneous Dirichlet or Neumann type boundary conditions. The wellposedness of the obtained initial value problem is proved and it is pointed out that each extension is compatible with the original boundary conditions. Accordingly,...

Note on a discretization of a linear fractional differential equation

Jan Čermák, Tomáš Kisela (2010)

Mathematica Bohemica

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The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.

On asymptotics of discrete Mittag-Leffler function

Luděk Nechvátal (2014)

Mathematica Bohemica

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The (modified) two-parametric Mittag-Leffler function plays an essential role in solving the so-called fractional differential equations. Its asymptotics is known (at least for a subset of its domain and special choices of the parameters). The aim of the paper is to introduce a discrete analogue of this function as a solution of a certain two-term linear fractional difference equation (involving both the Riemann-Liouville as well as the Caputo fractional h -difference operators) and describe...