Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term.
Yang, Qianqian, Liu, Fawang, Turner, Ian (2010)
International Journal of Differential Equations
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Displaying similar documents to “A finite difference approach for the initial-boundary value problem of the fractional Klein-Kramers equation in phase space”
Stability and convergence of an effective numerical method for the time-space fractional Fokker-Planck equation with a nonlinear source term.
Source terms identification for time fractional diffusion equation.
Murio, Diego, Mejía, Carlos E. (2008)
Revista Colombiana de Matemáticas
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On the numerical solution of fractional hyperbolic partial differential equations.
Ashyralyev, Allaberen, Dal, Fadime, Pinar, Zehra (2009)
Mathematical Problems in Engineering
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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.
Existence results for nonlinear fractional difference equation.
Chen, Fulai, Luo, Xiannan, Zhou, Yong (2011)
Advances in Difference Equations [electronic only]
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From Newton's equation to fractional diffusion and wave equations.
Vázquez, Luis (2011)
Advances in Difference Equations [electronic only]
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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 -difference operators) and describe...
An effective numerical method and its utilization to solution of fractional models used in bioengineering applications.
Petráš, Ivo (2011)
Advances in Difference Equations [electronic only]
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Multiplicity and uniqueness for a class of discrete fractional boundary value problems
Lv Zhanmei, Gong Yanping, Chen Yi (2014)
Applications of Mathematics
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The paper deals with a class of discrete fractional boundary value problems. We construct the corresponding Green's function, analyse it in detail and establish several of its key properties. Then, by using the fixed point index theory, the existence of multiple positive solutions is obtained, and the uniqueness of the solution is proved by a new theorem on an ordered metric space established by M. Jleli, et al. (2012).