This nine-chapter monograph introduces a rigorous investigation of q-difference operators in
standard and fractional settings. It starts with elementary calculus of q-differences and …

We prove that a linear q-difference equation of order n has a fundamental set of n-linearly
independent solutions. A q-type Wronskian is derived for the n-th order case extending the …

A q-SAMPLING THEOREM RELATED TO THE q-HANKEL TRANSFORM 1. Introduction The
classical sampling theorem asserts that every functio Page 1 PROCEEDINGS OF THE …

We will show that if the kernel K (x, t) in the representation f (t)=∫ a 0 K (x, t) u (t) dqt, with u∊
L 2 q (0, a), is a solution of a second-order q-Sturm–Liouville boundary problem, then f …

We establish a q-Titchmarsh-Weyl theory for singular q-Sturm-Liouville problems. We define
q-limit-point and q-limit circle singularities, and we give sufficient conditions which …

Geometric properties of the Jackson and Hahn–Exton q-Bessel functions are studied. For
each of them, three different normalizations are applied in such a way that the resulting …

Let I⊆ R be an interval and β: I→ I a strictly increasing and continuous function with a
unique fixed point s 0∈ I that satisfies (s 0− t)(β (t)− t)≥ 0 for all t∈ I, where the equality …

We investigate the asymptotic behavior of the eigenvalues and the eigenfunctions of q‐
Sturm‐Liouville eigenvalue problems. For this aim we study the asymptotic behavior of q …

Abstract Let\, I ⊆ R\, I⊆ R be an interval and\, β:\, I →\, I\, β: I→ I a strictly increasing and
continuous function with a unique fixed point\, s_0 ∈ I\, s 0∈ I that satisfies\,(s_0-t)(β (t)-t) ≥ …

We analyze spectral properties of the Hilbert L-matrix (1 max⁡(m, n)+ ν) m, n= 0∞ regarded
as an operator L ν acting on ℓ 2 (N 0), for ν∈ R, ν≠ 0,− 1,− 2,…. The approach is based on a …