Abstract
In this article, we present a nonlocal Neumann boundary value problems for separate sequential fractional symmetric Hahn integrodifference equation. The problem contains five fractional symmetric Hahn difference operators and one fractional symmetric Hahn integral of different orders. We employ Banach fixed point theorem and Schauder’s fixed point theorem to study the existence results of the problem.
Highlights
Quantum calculus is a study of calculus without limit that deals with a set of nondifferentiable functions
In 2009, Aldwoah [16,17] defined the right inverse of Dq,ω in the terms of both the Jackson q-integral containing the right inverse of Dq and Nörlund sum contaning the right inverse of ∆ω [18]
We study the boundary value problem involving functions F and H which separate fractional symmetric Hahn integral and fractional symmetric Hahn difference, and the boundary condition is a Neumann boundary condition that is assigned values at two non-local points
Summary
Quantum calculus is a study of calculus without limit that deals with a set of nondifferentiable functions. The study of the boundary value problems for fractional symmetric Hahn difference equation in the beginning, there exists only one paper on this subject [43]. We introduce the definitions of fractional symmetric Hahn difference calculus and its properties [41,42,43,44,45] as follows. Ω > 0, 0 < q < 1 and f defined on IqT,ω, the fractional symmetric Hahn difference operator of Riemann-Liouville type of order α is defined by. We use the definition of q, ω-symmetric analogue of the power function, Lemma 1 and Definition 2 to obtain
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