Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions

Ilic, M.; Liu, F.; Turner, I.; Anh, V.

The search session has expired. Please query the service again.

Displaying similar documents to “Numerical Approximation of a Fractional-In-Space Diffusion Equation (II) – with Nonhomogeneous Boundary Conditions”

Numerical Approximation of a Fractional-In-Space Diffusion Equation, I

Ilic, M., Liu, F., Turner, I., Anh, V. (2005)

Fractional Calculus and Applied Analysis

Similarity:

2000 Mathematics Subject Classification: 26A33 (primary), 35S15 (secondary) This paper provides a new method and corresponding numerical schemes to approximate a fractional-in-space diffusion equation on a bounded domain under boundary conditions of the Dirichlet, Neumann or Robin type. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of...

On the Operational Solution of a System of Fractional Differential Equations

Takači, Dj., Takači, A. (2010)

Fractional Calculus and Applied Analysis

Similarity:

MSC 2010: 26A33, 44A45, 44A40, 65J10 We consider a linear system of differential equations with fractional derivatives, and its corresponding system in the field of Mikusiński operators, written in a matrix form, by using the connection between the fractional and the Mikusiński calculus. The exact and the approximate operational solution of the corresponding matrix equations, with operator entries are determined, and their characters are analyzed. By using the packages...

Weak solutions to differential equations with left and right fractional derivatives defined on $ℝ$

T. M. Atanacković, S. Pilipović, B. Stanković (2009)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Similarity:

Fractional Calculus of the Generalized Wright Function

Kilbas, Anatoly (2005)

Fractional Calculus and Applied Analysis

Similarity:

Mathematics Subject Classification: 26A33, 33C20. The paper is devoted to the study of the fractional calculus of the generalized Wright function pΨq(z) defined for z ∈ C, complex ai, bj ∈ C and real αi, βj ∈ R (i = 1, 2, · · · p; j = 1, 2, · · · , q) by the series pΨq (z) It is proved that the Riemann-Liouville fractional integrals and derivative of the Wright function are also the Wright functions but of greater order. Special cases are considered. * The present...

Existence and uniqueness of fractional differential equations with integral boundary conditions.

Wang, Taige, Xie, Feng (2008)

The Journal of Nonlinear Sciences and its Applications

Similarity:

An equation in the left and right fractional derivatives of the same order

B. Stanković (2008)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Similarity:

An Expansion Formula for Fractional Derivatives and its Application

Atanackovic, T., Stankovic, B. (2004)

Fractional Calculus and Applied Analysis

Similarity:

An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is derived. The convergence of the series is proved and an estimate of the reminder is given. The form of the fractional derivative given here is especially suitable in deriving restrictions, in a form of internal variable theory, following from the second law of thermodynamics, when applied to linear viscoelasticity of fractional derivative type. ...

Linear Fractional PDE, Uniqueness of Global Solutions

Schäfer, Ingo, Kempfle, Siegmar, Nolte, Bodo (2005)

Fractional Calculus and Applied Analysis

Similarity:

Mathematics Subject Classification: 26A33, 47A60, 30C15. In this paper we treat the question of existence and uniqueness of solutions of linear fractional partial differential equations. Along examples we show that, due to the global definition of fractional derivatives, uniqueness is only sure in case of global initial conditions.

Positive solutions for boundary value problem of nonlinear fractional differential equation.

Qiu, Tingting, Bai, Zhanbing (2008)

The Journal of Nonlinear Sciences and its Applications

Similarity:

Discrete Models of Time-Fractional Diffusion in a Potential Well

Gorenflo, R., Abdel-Rehim, E. (2005)

Fractional Calculus and Applied Analysis

Similarity:

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99. By generalization of Ehrenfest’s urn model, we obtain discrete approximations to spatially one-dimensional time-fractional diffusion processes with drift towards the origin. These discrete approximations can be interpreted (a) as difference schemes for the relevant time-fractional partial differential equation, (b) as random walk models. The relevant convergence questions as well as the behaviour...

On the Riemann-Liouville Fractional q-Integral Operator Involving a Basic Analogue of Fox H-Function

Kalla, S., Yadav, R., Purohit, S. (2005)

Fractional Calculus and Applied Analysis

Similarity:

2000 Mathematics Subject Classification: 33D60, 26A33, 33C60 The present paper envisages the applications of Riemann-Liouville fractional q-integral operator to a basic analogue of Fox H-function. Results involving the basic hypergeometric functions like Gq(.), Jv(x; q), Yv(x; q),Kv(x; q), Hv(x; q) and various other q-elementary functions associated with the Riemann-Liouville fractional q-integral operator have been deduced as special cases of the main result.