Displaying similar documents to “Riesz potential operators and inverses via fractional centred derivatives.”

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...

Distributional fractional powers of the Laplacean. Riesz potentials

Celso Martínez, Miguel Sanzi, Francisco Periago (1999)

Studia Mathematica

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For different reasons it is very useful to have at one’s disposal a duality formula for the fractional powers of the Laplacean, namely, ( ( - Δ ) α u , ϕ ) = ( u , ( - Δ ) α ϕ ) , α ∈ ℂ, for ϕ belonging to a suitable function space and u to its topological dual. Unfortunately, this formula makes no sense in the classical spaces of distributions. For this reason we introduce a new space of distributions where the above formula can be established. Finally, we apply this distributional point of view on the fractional powers of...

A Poster about the Recent History of Fractional Calculus

Machado, Tenreiro, Kiryakova, Virginia, Mainardi, Francesco (2010)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22 In the last decades fractional calculus became an area of intense re-search and development. The accompanying poster illustrates the major contributions during the period 1966-2010.

A detailed analysis for the fundamental solution of fractional vibration equation

Li-Li Liu, Jun-Sheng Duan (2015)

Open Mathematics

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In this paper, we investigate the solution of the fractional vibration equation, where the damping term is characterized by means of the Caputo fractional derivative with the order α satisfying 0 < α < 1 or 1 < α < 2. Detailed analysis for the fundamental solution y(t) is carried out through the Laplace transform and its complex inversion integral formula. We conclude that y(t) is ultimately positive, and ultimately decreases monotonically and approaches zero for the case...