Displaying similar documents to “On q-Laplace Transforms of the q-Bessel Functions”

Krätzel Function as a Function of Hypergeometric Type

Kilbas, Anatoly, Saxena, R. K., Trujillo, Juan (2006)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 33C60, 33C20, 44A15 The paper is devoted to the study of the function Zνρ(x) defined for positive x > 0, real ρ ∈ R and complex ν ∈ C, being such that Re(ν) < 0 for ρ ≤ 0, [...] Such a function was earlier investigated for ρ > 0. Using the Mellin transform of Zνρ(x), we establish its representations in terms of the H-function and extend this function from positive x > 0 to complex z. The results obtained, being different...

An Analogue of Beurling-Hörmander’s Theorem for the Dunkl-Bessel Transform

Mejjaoli, Hatem (2006)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: Primary 35R10, Secondary 44A15 We establish an analogue of Beurling-Hörmander’s theorem for the Dunkl-Bessel transform FD,B on R(d+1,+). We deduce an analogue of Gelfand-Shilov, Hardy, Cowling-Price and Morgan theorems on R(d+1,+) by using the heat kernel associated to the Dunkl-Bessel-Laplace operator.

Integral Representations of Generalized Mathieu Series Via Mittag-Leffler Type Functions

Tomovski, Živorad (2007)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30 The main purpose of this paper is to present a number of potentially useful integral representations for the generalized Mathieu series as well as for its alternating versions via Mittag-Leffler type functions.

On the Generalized Confluent Hypergeometric Function and Its Application

Virchenko, Nina (2006)

Fractional Calculus and Applied Analysis

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2000 Mathematics Subject Classification: 26A33, 33C20 This paper is devoted to further development of important case of Wright’s hypergeometric function and its applications to the generalization of Γ-, B-, ψ-, ζ-, Volterra functions.

Polynomial Expansions for Solutions of Higher-Order Bessel Heat Equation in Quantum Calculus

Ben Hammouda, M.S., Nemri, Akram (2007)

Fractional Calculus and Applied Analysis

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Mathematics Subject Class.: 33C10,33D60,26D15,33D05,33D15,33D90 In this paper we give the q-analogue of the higher-order Bessel operators studied by I. Dimovski [3],[4], I. Dimovski and V. Kiryakova [5],[6], M. I. Klyuchantsev [17], V. Kiryakova [15], [16], A. Fitouhi, N. H. Mahmoud and S. A. Ould Ahmed Mahmoud [8], and recently by many other authors. Our objective is twofold. First, using the q-Jackson integral and the q-derivative, we aim at establishing some properties...

Spectrum of Functions for the Dunkl Transform on R^d

Mejjaoli, Hatem, Trimèche, Khalifa (2007)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 42B10 In this paper, we establish real Paley-Wiener theorems for the Dunkl transform on R^d. More precisely, we characterize the functions in the Schwartz space S(R^d) and in L^2k(R^d) whose Dunkl transform has bounded, unbounded, convex and nonconvex support.

Fractional Integration of the Product of Bessel Functions of the First Kind

Kilbas, Anatoly, Sebastian, Nicy (2010)

Fractional Calculus and Applied Analysis

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Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09 Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for...

On the Mellin Transforms of Dirac’S Delta Function, The Hausdorff Dimension Function, and The Theorem by Mellin

Südland, Norbert, Baumann, Gerd (2004)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 44A05, 46F12, 28A78 We prove that Dirac’s (symmetrical) delta function and the Hausdorff dimension function build up a pair of reciprocal functions. Our reasoning is based on the theorem by Mellin. Applications of the reciprocity relation demonstrate the merit of this approach.