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

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, ω 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.

Existence Results of a Nonlocal Fractional Symmetric Hahn Integrodifference Boundary Value Problem

“…In 2020, Soontharanon and Sitthiwirattham [33] introduced fractional (p, q)-calculus and its properties. For some recent developments in fractional calculus, see [34][35][36][37][38][39][40][41][42][43][44][45] and the references cited therein.…”

Taylor theory associated with Hahn difference operator

“…Hahn difference operator unifies the two most well-known quantum difference operators: the Jackson q-difference operator [11][12][13], which is defined by D q f (t) = f (qt)f (t) t(q -1) , if t = 0, 0 < q < 1; (1.2) and the forward difference ω , which is defined by ω f (t) = f (t + ω)f (t) ω , t ∈ R, ω > 0, (1.3) see [4,5,14,15]. Hahn operator has attracted the attention of several researchers and a variety of results can be found in papers [1,2,6,[16][17][18][19][20][21][22]. In [3] Annaby and Mansour proved analytically the q-Taylor series associated with D q , introduced by Jackson [12], of an analytic function in some complex domain.…”

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).…”