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 …

This paper is devoted for a rigorous investigation of Hahn's difference operator and the
associated calculus. Hahn's difference operator generalizes both the difference operator …

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 …

In this article, we discuss a conformable fractional Sturm‐Liouville boundary‐value problem.
We prove an existence and uniqueness theorem for this equation and formulate a self …

This chapter introduces a comprehensive study for Sturm–Liouville theory of the q, ω-Hahn
difference operators in the regular setting. We define a Hilbert space of q, ω-square …

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 …

In this paper, a 𝑞-analogue of the Sturm–Liouville problem with discontinuity condition on a
finite interval is studied. It is proved that the 𝑞-Sturm–Liouville problem with discontinuity …

In this paper, we studied q-analogue of Sturm-Liouville boundary value problem on a finite
interval having a discontinuity in an interior point. We proved that the q-Sturm-Liouville …

Starting on the basis of q-symmetric oscillator algebra and on the associated q-calculus
properties, we study a deformed quantum mechanics defined in the framework of the basic …

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 …