In this survey talk we aim to clarify the close relationships between the operators of the generalized fractional calculus (GFC), some classes of generalized hypergeo-metric functions and generalizations of the classical integral transforms. The GFC developed in [1] is based on the essential use of the Special Functions (SF). The generalized (multiple) fractional integrals and derivatives are d...

In this paper, we show that the matrix elements of some Lorentz group representation operators and bases transform acting in space may be expressed terms modified Bessel–Clifford functions their multi-index analogs introduced by authors via Delerue hyper Bessel functions.

We study integrals of the type ∫ t 0 φ(s)dLs, where φ is a positive locally bounded Borel function and Lt denotes the local time at level 0 of a Bessel process of dimension d, 0 < d < 2. 1991 Mathematics Subject Classifications : 60J65, 60J55, 45E10.

Named essentially after their close relationship with the modified Bessel function K?(z) of second kind, which is known also as Macdonald (or, a slightly different definition, Basset function), so-called polynomials yn(x) and generalized yn(x;?,?) stemmed naturally in some systematic investigations classical wave equation spherical polar coordinates. Our main purpose this invited survey-cum-exp...

The electromagnetic interaction between a circular disk with finite conductivity and thickness coaxial loop of constant current is addressed here. the material lead to adoption suitable generalized boundary conditions, problem thereby reduced solution two sets dual integral equations in Hankel transform domain. Such are then solved by expanding spectral unknowns Neumann series Bessel functions....

In memoriam Csörgő Sándor, dear friend and great scholar Keywords: Bessel function of first kind J ν (z) Bounds for J ν (z) Positive zeros j ν,s of J ν (z) Generalized Kapteyn expansion Kapteyn series a b s t r a c t A new inequality is derived for the Bessel function of the first kind J ν (z), ν ∈ R, and a discussion of the consequent convergence is given for the generalized Kapteyn-type expan...

Virginia Kiryakova Dedicated to the 75th anniversary of Professor Gary Roach Abstract A generalization of the Poisson-type integral transformation proposed by Dimovski is applied to hyper-Bessel differential equations of arbitrary order, as a transmutation operator. By this method, their solutions are written in an explicit form, by evaluating operators of the generalized fractional calculus of...