Abstract
In this paper, we study a nonlocal Robin boundary value problem for fractional Hahn integrodifference equation. Our problem contains three fractional Hahn difference operators and a fractional Hahn integral with different numbers of q, omega and order. The existence and uniqueness result is proved by using the Banach fixed point theorem. In addition, the existence of at least one solution is obtained by using Schauder’s fixed point theorem.
Highlights
Many researchers have extensively studied calculus without limit that deals with a set of non-differentiable functions, the so-called quantum calculus
We study the Hahn quantum calculus that is one type of quantum calculus
There are apparently few research works related to boundary value problems of fractional Hahn difference equations
Summary
Many researchers have extensively studied calculus without limit that deals with a set of non-differentiable functions, the so-called quantum calculus. Patanarapeelert et al [35] studied the boundary value problem for fractional Hahn difference equation containing a sequential Caputo fractional Hahn integrodifference equation with nonlocal Dirichlet boundary conditions. There are apparently few research works related to boundary value problems of fractional Hahn difference equations (see [34, 35]). In this paper, we devote ourselves to studying a boundary value problem for fractional Hahn difference equation. Lemma 2.9 ([37] Schauder’s fixed point theorem) Let (D, d) be a complete metric space, U be a closed convex subset of D, and T : D → D be the map such that the set Tu : u ∈ U is relatively compact in D.
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