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 q-Taylor series for Jackson q-difference operators. Absolute and uniform
convergence to the original function are proved for analytic functions. We derive …

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 Whittaker-Shannon-Kotel’nikov sampling theorem related to the Askey-Wilson functions Page
1 Journal of Nonlinear Mathematical Physics Volume 14, Number 3 (2007), 375–388 Article A …

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 …

Basic Fourier transform on the space of entire functions of logarithm order 2 | Advances in
Continuous and Discrete Models Skip to main content SpringerLink Account Menu Find a journal …

This chapter includes proofs of the existence and uniqueness of the solutions of first order
systems of q-difference equations in a neighborhood of a point a, a ≧ 0. Then, as …

This paper is a collection of q analogue of various classical methods for finding solutions of
algebraic and transcendental equations. It also deals with comparing classical methods with …

It is shown that the q-Taylor series corresponding to Jackson's q-difference operator can be
generated by the Newton interpolation formulae and the related remainders can be …

This paper is a collection of q analogue of various problems. It also aims at focusing on work
performed by various researchers and describes q analogues of various functions. We have …