Journal Article10.1134/S0965542506100149
Difference methods for solving boundary value problems for fractional differential equations
79
TL;DR: In this paper, the stability and convergence of difference schemes for second-order ordinary and partial differential equations with a fractional time derivative were proved for the diffusion equation in one-and multidimensional domains.
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Abstract: Difference schemes for second-order ordinary and partial differential equations with a fractional time derivative are considered. Stationary and nonstationary problems for the diffusion equation in one-and multidimensional domains are examined separately. The stability and convergence of the difference schemes for these equations are proved.
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Citations
A new difference scheme for the time fractional diffusion equation
TL;DR: A new difference analog of the Caputo fractional derivative (called the L 2 - 1 σ formula) is constructed and some difference schemes generating approximations of the second and fourth order in space and the second order in time for the time fractional diffusion equation with variable coefficients are considered.
772
A Priori Estimates for Solutions of Boundary Value Problems for Fractional-Order Equations
TL;DR: In this article, the authors considered boundary value problems of the first and third kind for the diffusion wave equation and used the method of energy inequalities to find a priori estimates for the solutions.
261
A Priori Estimates for Solutions of Boundary Value Problems for Fractional-Order Equations
TL;DR: In this paper, the authors considered boundary value problems of the first and third kind for the diffusion wave equation and used the method of energy inequalities to find a priori estimates for the solutions.
189
Numerical approximations for fractional diffusion equations via a Chebyshev spectral-tau method
TL;DR: An accurate and efficient spectral tau technique for solving the fractional diffusion equations numerically based upon Chebyshev tau approximation together with Chebysheev operational matrix of Caputo fractional differentiation is proposed.
40
Quadratic spline solution for boundary value problem of fractional order
Waheed K. Zahra,Samah M. Elkholy +1 more
TL;DR: A consistency relation is derived which can be used for computing approximation to the solution for this class of boundary value problems of fractional order and four numerical examples are included to illustrate the practical usefulness of the proposed method.
36
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