In this paper, the method of transmutation operators is used to construct an exact solution Goursat problem for a fourth-order hyperbolic equation with singular Bessel operator. We emphasise that in many other papers and monographs fractional Erdélyi-Kober are as integral operators, but our approach them additional new properties important applications. Specifically, it extends its applications...

The method of partial Fourier transform is used to find explicit formulas for two remarkable fundamental solutions for a generalized Tricomi operator. These fundamental solutions reflect clearly the mixed type of the Tricomi operator. In proving these results, we establish explicit formulas for Fourier transforms of some functions involving Bessel functions.

Abstract Integrable operators arise in random matrix theory, where they describe the asymptotic eigenvalue distribution of large self-adjoint random matrices from the generalized unitary ensembles. This paper gives sufficient conditions for an integrable operator to be the square of a Hankel operator, and applies the condition to the Airy, associated Laguerre, modified Bessel and Whittaker func...

In this paper, we consider the non-homogeneous wave equation generated by Bessel operator. We prove existence and uniqueness of solution The representation is given. obtained a priori estimates in Sobolev type space. This problem was firstly considered work M. Assal [1] setting Bessel-Kingman hypergroups. technique used based on convolution theorem related estimates. Here, use different approac...

Abstract This paper deals with Al-Salam fractional q -integral operator and its application to certain -analogues of Bessel functions power series. has been applied various types -Bessel some series special type. It obtained for basic -generating series, -exponential -trigonometric as well. Various results corollaries are provided an this theory.

A reproducing kernel Hilbert space (RKHS) approximation problem arising from learning theory is investigated. Some K-functionals and moduli of smoothness with respect to RKHSs are defined Fourier–Bessel series transforms, respectively. Their equivalent relation shown, which the upper bound estimate for best RKHS provided. The convergence rate bounded modulus smoothness, shows that can attain sa...

If B < ∞ we call F = {fi}i∈I a Bessel sequence with Bessel bound B. If 0 < A ≤ B < ∞, then {fi}i∈I is a frame for K. If K 6= H we call {fi}i∈I a frame sequence in H. The largest A and the smallest B satisfying the above inequalities are called the optimal lower and upper frame bound and will be denoted A(F) and B(F) respectively. If A = B = λ we call this a λ-tight frame and if λ = 1 it is call...