Displaying similar documents to “A modified quasi-boundary value method for the backward time-fractional diffusion problem”

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...

Solving Fractional Diffusion-Wave Equations Using a New Iterative Method

Daftardar-Gejji, Varsha, Bhalekar, Sachin (2008)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 31B10 In the present paper a New Iterative Method [1] has been employed to find solutions of linear and non-linear fractional diffusion-wave equations. Illustrative examples are solved to demonstrate the efficiency of the method. * This work has partially been supported by the grant F. No. 31-82/2005(SR) from the University Grants Commission, N. Delhi, India.

Global existence and blow-up of generalized self-similar solutions for a space-fractional diffusion equation with mixed conditions

Farid Nouioua, Bilal Basti (2021)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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This paper investigates the problem of the existence and uniqueness of solutions under the generalized self-similar forms to the space-fractional diffusion equation. Therefore, through applying the properties of Schauder's and Banach's fixed point theorems; we establish several results on the global existence and blow-up of generalized self-similar solutions to this equation.

Anomalous diffusion phenomena: A kinetic approach

Antoine Mellet (2014-2015)

Séminaire Laurent Schwartz — EDP et applications

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In this talk, we review some aspects of the derivation of fractional diffusion equations from kinetic equations and in particular some applications to the description of anomalous energy transport in FPU chains. This is based on joint works with N. Ben Abdallah, L. Cesbron, S. Merino, S. Mischler, C. Mouhot and M. Puel

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...

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,...

Positive solutions for Hadamard differential systems with fractional integral conditions on an unbounded domain

Tariboon Jessada, Sotiris K. Ntouyas, Suphawat Asawasamrit, Chanon Promsakon (2017)

Open Mathematics

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In this paper, we investigate the existence of positive solutions for Hadamard type fractional differential system with coupled nonlocal fractional integral boundary conditions on an infinite domain. Our analysis relies on Guo-Krasnoselskii’s and Leggett-Williams fixed point theorems. The obtained results are well illustrated with the aid of examples.