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Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation

Nikolova, Yanka, Boyadjiev, Lyubomir (2010)

Fractional Calculus and Applied Analysis

Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12.The method of integral transforms based on using a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problem for the time-space fractional diffusion equation expressed in terms of the Caputo time-fractional derivative and a generalized Riemann-Liouville space-fractional derivative.

Integrals and Banach spaces for finite order distributions

Erik Talvila (2012)

Czechoslovak Mathematical Journal

Let c denote the real-valued functions continuous on the extended real line and vanishing at - . Let r denote the functions that are left continuous, have a right limit at each point and vanish at - . Define 𝒜 c n to be the space of tempered distributions that are the n th distributional derivative of a unique function in c . Similarly with 𝒜 r n from r . A type of integral is defined on distributions in 𝒜 c n and 𝒜 r n . The multipliers are iterated integrals of functions of bounded variation. For each n , the spaces...

Integration of some very elementary functions

Jan Mařík (1993)

Mathematica Bohemica

Let m be a natural number. Let f , g and Q be real polynomials such that { d e g f , d e g g } { 1 , 2 } , d e g Q < m d e g f , g is not a square and f has imaginary roots, if it is not linear. Effective methods for the integration of Q / ( f m g are exhibited.

Interior sphere property of attainable sets and time optimal control problems

Piermarco Cannarsa, Hélène Frankowska (2006)

ESAIM: Control, Optimisation and Calculus of Variations

This paper studies the attainable set at time T>0 for the control system y ˙ ( t ) = f ( y ( t ) , u ( t ) ) u ( t ) U showing that, under suitable assumptions on f, such a set satisfies a uniform interior sphere condition. The interior sphere property is then applied to recover a semiconcavity result for the value function of time optimal control problems with a general target, and to deduce C1,1-regularity for boundaries of attainable sets.

Interpolated inequalities between exponential and Gaussian, Orlicz hypercontractivity and isoperimetry.

Franck Barthe, Patrick Cattiaux, Cyril Roberto (2006)

Revista Matemática Iberoamericana

We introduce and study a notion of Orlicz hypercontractive semigroups. We analyze their relations with general F-Sobolev inequalities, thus extending Gross hypercontractivity theory. We provide criteria for these Sobolev type inequalities and for related properties. In particular, we implement in the context of probability measures the ideas of Maz'ja's capacity theory, and present equivalent forms relating the capacity of sets to their measure. Orlicz hypercontractivity efficiently describes the...

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