Displaying similar documents to “Fractional powers of closed operators”

Generalized Fractional Calculus, Special Functions and Integral Transforms: What is the Relation? Обобщения на дробното смятане, специалните функции и интегралните трансформации: Каква е връзката?

Kiryakova, Virginia (2011)

Union of Bulgarian Mathematicians

Similarity:

Виржиния С. Кирякова - В този обзор илюстрираме накратко наши приноси към обобщенията на дробното смятане (анализ) като теория на операторите за интегриране и диференциране от произволен (дробен) ред, на класическите специални функции и на интегралните трансформации от лапласов тип. Показано е, че тези три области на анализа са тясно свързани и взаимно индуцират своето възникване и по-нататъшно развитие. За конкретните твърдения, доказателства и примери, вж. Литературата. ...

Distributional fractional powers of the Laplacean. Riesz potentials

Celso Martínez, Miguel Sanzi, Francisco Periago (1999)

Studia Mathematica

Similarity:

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...

α-Mellin Transform and One of Its Applications

Nikolova, Yanka (2012)

Mathematica Balkanica New Series

Similarity:

MSC 2010: 35R11, 44A10, 44A20, 26A33, 33C45 We consider a generalization of the classical Mellin transformation, called α-Mellin transformation, with an arbitrary (fractional) parameter α > 0. Here we continue the presentation from the paper [5], where we have introduced the definition of the α-Mellin transform and some of its basic properties. Some examples of special cases are provided. Its operational properties as Theorem 1, Theorem 2 (Convolution theorem) and Theorem...

Some fractional integral formulas for the Mittag-Leffler type function with four parameters

Praveen Agarwal, Juan J. Nieto (2015)

Open Mathematics

Similarity:

In this paper we present some results from the theory of fractional integration operators (of Marichev- Saigo-Maeda type) involving the Mittag-Leffler type function with four parameters ζ , γ, Eμ, ν[z] which has been recently introduced by Garg et al. Some interesting special cases are given to fractional integration operators involving some Special functions.

A detailed analysis for the fundamental solution of fractional vibration equation

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

Open Mathematics

Similarity:

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...

On Fractional Helmholtz Equations

Samuel, M., Thomas, Anitha (2010)

Fractional Calculus and Applied Analysis

Similarity:

MSC 2010: 26A33, 33E12, 33C60, 35R11 In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.