Displaying similar documents to “Maximum Principle and Its Application for the Time-Fractional Diffusion Equations”

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...

System of fractional differential equations with Erdélyi-Kober fractional integral conditions

Natthaphong Thongsalee, Sorasak Laoprasittichok, Sotiris K. Ntouyas, Jessada Tariboon (2015)

Open Mathematics

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In this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.

IVPs for singular multi-term fractional differential equations with multiple base points and applications

Yuji Liu, Pinghua Yang (2014)

Applicationes Mathematicae

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The purpose of this paper is to study global existence and uniqueness of solutions of initial value problems for nonlinear fractional differential equations. By constructing a special Banach space and employing fixed-point theorems, some sufficient conditions are obtained for the global existence and uniqueness of solutions of this kind of equations involving Caputo fractional derivatives and multiple base points. We apply the results to solve the forced logistic model with multi-term...

Fractional Derivatives in Spaces of Generalized Functions

Stojanović, Mirjana (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 46Fxx, 58C05 Dedicated to 80-th birthday of Prof. Rudolf Gorenflo We generalize the two forms of the fractional derivatives (in Riemann-Liouville and Caputo sense) to spaces of generalized functions using appropriate techniques such as the multiplication of absolutely continuous function by the Heaviside function, and the analytical continuation. As an application, we give the two forms of the fractional derivatives of discontinuous functions in spaces of...

On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)

Małgorzata Klimek (2011)

Banach Center Publications

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One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.