Fractional diffusion equation in half-space with Robin boundary condition

Duan, Jun‐Sheng; Wang, Zhong; Fu, Shouzhong

doi:10.2478/s11534-013-0206-4

Cited by 2 publications

(2 citation statements)

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“…In [20] an infinite solid with spherical cavity was considered under Dirichlet and mathematical Neumann boundary conditions, whereas the corresponding problem under Robin boundary condition was studied in [29]. The fractional diffusion-wave equation in a half-line and half-space under Robin boundary condition was considered by the author [24,28] and later on in [4]. Existence and uniqueness of solutions to a general class of time-nonlocal problems with mathematical Robin boundary condition was studied in [35].…”

Section: Introductionmentioning

confidence: 99%

Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

Povstenko¹

2014

Open Mathematics

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The central symmetric time-fractional heat conduction equation with Caputo derivative of order 0 < α ≤ 2 is considered in a ball under two types of Robin boundary condition: the mathematical one with the prescribed linear combination of values of temperature and values of its normal derivative at the boundary, and the physical condition with the prescribed linear combination of values of temperature and values of the heat flux at the boundary, which is a consequence of Newton’s law of convective heat exchange between a body and the environment. The integral transform technique is used. Numerical results are illustrated graphically.

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Section: Introductionmentioning

confidence: 99%

Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

Povstenko¹

2014

Open Mathematics

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“…In, [23], the fractional diffusion equation in half-space was subject to the homogeneous Dirichlet boundary condition and the homogeneous Neumann boundary condition. The fractional diffusion equation in halfspace with the Robin boundary condition was considered in, [24]. Using the integral transform methods, including the Laplace transform and the Fourier transform it was obtained the exact solution of the problem.…”

Section: Formulation Of the Problemsmentioning

confidence: 99%

Problem of Determining the Density of Sources in a Multidimensional Heat Equation with the Caputo Time Fractional Derivative

Durdiev

2023

1790-5044

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In this paper, we propose a new formula for representing the solution of the third initial-boundary value problem for multidimensional fractional heat equation with the Caputo derivative. This formula is obtained by the continuation method used in the theory of partial differential equations with integer derivatives. The Green’s function of the problem is also constructed in terms of the Fox H- function. Involving the results of solving a direct problem and the overdetermination condition, a uniqueness theorem for the definition of the spatial part of the multidimensional source function is proved.

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Fractional diffusion equation in half-space with Robin boundary condition

Cited by 2 publications

References 20 publications

Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

Fundamental solutions to the fractional heat conduction equation in a ball under Robin boundary condition

Problem of Determining the Density of Sources in a Multidimensional Heat Equation with the Caputo Time Fractional Derivative

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