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 …

The theory of reproducing kernels started with two papers of 1921 [449] and 1922 [45] which
dealt with typical reproducing kernels of Szegö and Bergman, and since then the theory has …

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 …

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 …

In this paper, we define a q-Sturm Liouville problem with discontinuity conditions and prove
that it is self adjoint in L2 (0, π). We show that eigenfunctions of this problem are in the form …

In this paper, we discuss the existence of solutions for impulsive fractional q-integro-
difference equations with separated boundary conditions. Existence results are proved via …

In this paper, we study the boundary value problem of a class of nonlinear fractional q-
difference equations with parameter involving the Riemann-Liouville fractional derivative. By …

In this paper, we study the boundary value problem of a fractional q-difference equation with
nonlocal conditions involving the fractional q-derivative of the Caputo type, and the …

In this paper, we formulate a regular q-fractional Sturm–Liouville problem (qFSLP) which
includes the left-sided Riemann–Liouville and the right-sided Caputo q-fractional derivatives …