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 …

A variety of coherent states of the harmonic oscillator is considered. It is formed by a
particular superposition of canonical coherent states. In the simplest case, these …

We continue our previous application of supersymmetric quantum mechanical methods to
eigenvalue problems in the context of some deformed canonical commutation relations …

Two generalizations of Kempf's quadratic canonical commutation relation in one dimension
are considered. The first one is the most general quadratic commutation relation. The …

We study the behavior of the eigenvalues of the one and two dimensions of q‐deformed
Dirac oscillator. The eigensolutions have been obtained by using a method based on the q …

In this paper, we study dissipative q-Sturm—Liouville operators in Weyl's limit circle case.
We describe all maximal dissipative, maximal accretive, self adjoint extensions of q-Sturm …

As in the classical theory of ordinary fractional differential equations, q-difference equations
of fractional order are divided into linear, nonlinear, homogeneous, and inhomogeneous …

In this paper, we solved the Schrödinger equation in the commutative and non-commutative
(NC) spaces under the presence of magnetic field. In other words, we obtained the energy …

In this chapter we investigate q-analogues of the classical fractional calculi. We study the q-
Riemann–Liouville fractional integral operator introduced by Al-Salam (Proc. Am. Math. Soc …

Spectra of the most general Hermitian Hamiltonian which is bilinear in the creation and
annihilation operators of a q-harmonic oscillator are investigated with the help of the …