Abstract In this paper, we prove the equivalence between a K-functional and modulus of smoothness generated by Laguerre-Bessel operator on

This paper deals with the design fractional solution of Bessel equation. We obtain explicit solutions of the equation with the help of fractional calculus techniques. Using the N-fractional calculus operator N(ν) method, we derive the fractional solutions of the equation.

This paper aims to study the q-wavelet and the q-wavelet transforms, associated with the q-Bessel operator for a fixed q ∈]0, 1[. As an application, an inversion formulas of the q-Riemann-Liouville and q-Weyl transforms using qwavelets are given. For this purpose, we shall attempt to extend the classical theory by giving their q-analogues.

We explore the connections between singular Weyl–Titchmarsh theory and the single and double commutation methods. In particular, we compute the singular Weyl function of the commuted operators in terms of the original operator. We apply the results to spherical Schrödinger operators (also known as Bessel operators). We also investigate the connections with the generalized Bäcklund–Darboux trans...

In this work we consider an initial one-point boundary value problem to the heat equation with the Bessel operator ut − (uxx + 1 xux) = |u| p−2u. We first prove a local existence result. Then we show that the solution blows up in finite time.

This paper aims to study the q-wavelet and the q-wavelet transforms, associated with the q-Bessel operator for a fix q ∈]0, 1[. As application, an inversion formulas of the q-Riemann-Liouville and q-Weyl transforms using q-wavelets are given. For this purpose, we shall attempt to extend the classical theory by giving their q-analogues.

Let 1 < p, q < ∞ and s, r ∈ R. It is proved that any function in the amalgam space W (H p′(R ), l∞), where p ′ is the conjugate exponent to p and H p′(R ) is the Bessel potential space, defines a bounded pointwise multiplication operator in the modulation space M p,q(R ), whenever r > |s|+ d.