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