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 …

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In this paper, we introduce the polynomials B n, α (k)(x; q) generated by a function including
Jackson q-Bessel functions J α (k)(x; q)(k= 1, 2, 3), α>-1. The cases α=±1 2 are the q …

In this paper we derive the nonlinear recurrence relation for the recursion coefficients βn of
polynomials orthogonal with respect to q-analogues of Freud exponential weights. An …

A method has been introduced recently for deriving indefinite integrals of special functions
that satisfy homogeneous (nonhomogeneous) second-order linear differential equations …

We study in this paper, a one parameter deformation of the q-Laguerre weight function. An
investigation is made on the polynomials orthogonal with respect to such a weight. With the …

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

A Lagrangian method is introduced recently for deriving indefinite integrals of special
functions that satisfy homogeneous (nonhomogeneous) second-order linear differential …

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 …

These lectures contain a brief introduction to orthogonal polynomials with some applications
to nonlinear recurrence relation. We discuss the spectral theory of orthogonal polynomials …