Displaying similar documents to “Existence and uniqueness of the solution for a time-fractional diffusion equation with Robin boundary condition.”

Maximum Principle and Its Application for the Time-Fractional Diffusion Equations

Luchko, Yury (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 33E12, 35B45, 35B50, 35K99, 45K05 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary In the paper, maximum principle for the generalized time-fractional diffusion equations including the multi-term diffusion equation and the diffusion equation of distributed order is formulated and discussed. In these equations, the time-fractional derivative is defined in the Caputo sense. In contrast to the Riemann-Liouville fractional derivative,...

Nonlinear Time-Fractional Differential Equations in Combustion Science

Pagnini, Gianni (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 34A08 (main), 34G20, 80A25 The application of Fractional Calculus in combustion science to model the evolution in time of the radius of an isolated premixed flame ball is highlighted. Literature equations for premixed flame ball radius are rederived by a new method that strongly simplifies previous ones. These equations are nonlinear time-fractional differential equations of order 1/2 with a Gaussian underlying diffusion process. Extending the analysis to self-similar...

Professor Rudolf Gorenflo and his Contribution to Fractional Calculus

Luchko, Yury, Mainardi, Francesco, Rogosin, Sergei (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33 Dedicated to Professor Rudolf Gorenflo on the occasion of his 80th anniversary This paper presents a brief overview of the life story and professional career of Prof. R. Gorenflo - a well-known mathematician, an expert in the field of Differential and Integral Equations, Numerical Mathematics, Fractional Calculus and Applied Analysis, an interesting conversational partner, an experienced colleague, and a real friend. Especially his role in the modern Fractional...

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

Yuriy Povstenko (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...

A modified quasi-boundary value method for the backward time-fractional diffusion problem

Ting Wei, Jun-Gang Wang (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this paper, we consider a backward problem for a time-fractional diffusion equation with variable coefficients in a general bounded domain. That is to determine the initial data from a noisy final data. Based on a series expression of the solution, a conditional stability for the initial data is given. Further, we propose a modified quasi-boundary value regularization method to deal with the backward problem and obtain two kinds of convergence rates by using an regularization parameter...