Integral Transforms and Special Functions 

About: Integral Transforms and Special Functions is an academic journal published by Taylor & Francis. The journal publishes majorly in the area(s): Orthogonal polynomials & Classical orthogonal polynomials. It has an ISSN identifier of 1065-2469. Over the lifetime, 1804 publications have been published receiving 19795 citations.

Generalized mittag-leer function and generalized fractional calculus operators

Abstract: The paper is devoted to the study of the function E γ ρ,μ(z) defined for complex ρ, μ, γ (Re(ρ) > 0) by which is a generalization of the classical Mittag-Leffler function E ρ,μ(z) and the Kummer confluent hypergeometric function Φ(γ, μ; z). The properties of E γ ρ,μ(z) including usual differentiation and integration, and fractional ones are proved. Further the integral operator with such a function kernel is studied in the space L(a, b). Compositions of the Riemann–Liouville fractional integration and differentiation operators with E γ ρ,μ,ω;a+ are established. An analogy of the semigroup property for the composition of two such operators with different indices is proved, and the results obtained are applied to construct the left inversion operator to the operator E γ ρ,μ,ω;a+. Since, for γ = 0, E 0 ρ,μ,ω;a+ coincides with the Riemann–Liouville fractional integral of order μ, the above operator and its inversion can be considered as generalized fractional calculus operators involving the generalized Mitta...

Integration and differentiation to a variable fractional order

Abstract: Interpretation and differentiation of functions to a variable order (d/dx)nf(x) is studied in two ways: 1) using the Riemann-Liouville definition, 2) using Fourier transforms Some properties and the inversion formula are obtained

Completely monotonic functions

Abstract: In this expository article we survey some properties of completely monotonic functions and give various examples, including some famous special functions. Such function are useful, for example, in probability theory. It is known, [1, p.450], for example, that a function w is the Laplace transform of an infinitely divisible probability distribution on (0,∞), if and only if w = e-h , where the derivative of h is completely monotonic and h(0+) = 0.

Certain Subclasses of Analytic Functions Associated with the Generalized Hypergeometric Function

Abstract: Recently, the authors introduced and studied certain subclasses of analytic functions (associated with the generalized hypergeometric function) using the classical normalization. The main object of this sequel to the earlier work is to present a systematic investigation of various subclasses of analytic functions using Montel's normalization. Coefficients estimates, distortion theorems, and the radii of convexity and starlikeness for each of these classes are given.

On a progress in the theory of lebesgue spaces with variable exponent: maximal and singular operators

Abstract: This paper represents a broadened version of the plenary lecture presented by the author at the conference Analytic Methods of Analysis and Differential Equations (AMADE-2003), September 4–9, 2003,...