On a nonlocal boundary value problem for nonlinear second-order Hahn difference equation with two different q , ω $q,\omega$ -derivatives

Abstract

In this paper, we study a nonlocal boundary value problem for a second-order Hahn difference equation. Our problem contains two Hahn difference operators with different numbers of q and ω. An existence and uniqueness result is proved by using the Banach fixed point theorem, and the existence of a positive solution is established by using the Krasnoselskii fixed point theorem. MSC: 39A10; 39A13; 39A70Keywords: Hahn difference equations; boundary value problems; positive solution; existence IntroductionThe quantum calculus, also known as the calculus without considering limits, deals with sets of nondifferentiable functions. There are many different types of quantum difference operators, for example, the Jackson q-difference operator, the forward (delta) difference operator, the backward (nabla) difference operator, and so on. These operators are found in many applications of mathematical areas such as orthogonal polynomials, basic hypergeometric functions, combinatorics, the calculus of variations, the theory of relativity, hypergeometric series, complex analysis, particle physics, and quantum mechanics. For some recent results and applications of the quantum calculus, see [-] and the references therein.In , Hahn [] introduced the Hahn difference operator D q,ω ,The Hahn difference operator is generalized to two well-known difference operators, the forward difference operator and the Jackson q-difference operator. Notice that, under appropriate conditions,whenever ω = , and

Impulsive fractional quantum Hahn difference boundary value problems

“…[11][12][13][14]). For some recent results on the boundary value problems of Hahn difference equations we refer to [15][16][17][18][19] and references therein. Let us emphasize that the definition (3) does not remain valid for impulse points t k , k ∈ Z, such that t k ∈ (qt, t).…”

The spectral expansion for the Hahn–Dirac system on the whole line

“…In 2016, Hamza and Makharesh [17] investigated Leibniz's rule and Fubini's theorem in association with the Hahn difference operator. Sitthiwirattham [26] investigated the nonlocal boundary value problem for nonlinear Hahn difference equations. Recently, in [9], the regular Hahn-Sturm-Liouville problem was studied.…”

On nonlocal Robin boundary value problems for Riemann–Liouville fractional Hahn integrodifference equation

“…In 2016, Hamza and Makharesh [25] investigated the Leibnitz's rule and Fubini's theorem associated with Hahn difference operator. In the same year, Sitthiwirattham [26] where 0 < q < 1, 0 < ω < T, ω 0 :=…”