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

Rujira Ouncharoen,Nichaphat Patanarapeelert,Thanin Sitthiwirattham

doi:10.3390/sym13112174

Abstract

The existence of solutions of nonlocal fractional symmetric Hahn integrodifference boundary value problem is studied. We propose a problem of five fractional symmetric Hahn difference operators and three fractional symmetric Hahn integrals of different orders. We first convert our nonlinear problem into a fixed point problem by considering a linear variant of the problem. When the fixed point operator is available, Banach and Schauder’s fixed point theorems are used to prove the existence results of our problem. Some properties of (q,ω)-integral are also presented in this paper as a tool for our calculations. Finally, an example is also constructed to illustrate the main results.

Highlights

Quantum calculus has been proposed in the last three decades
Using Banach fixed point theorem, we first let C = C Iq,ω function u with the norm defined by ν ν +1
The new knowledge of fractional symmetric Hanh calculus was used in the studying of existence results of the nonlocal fractional symmetric Hahn integrodifference boundary value problems

Summary

Introduction

The q-calculus, one type of quantum presented by Jackson [1,2], has been extensively used in the studies of mechanics, calculus of variations, and other problems in physics [3,4,5,6,7,8,9,10,11,12,13]). Presented the development of quantum calculus based on two parameters q and ω, which is called Hahn calculus. Hahn operator was widly employed in many studies such as variational calculus [17,18,19], the initial value problems [20,21,22], the boundary value problems [23,24], and families of orthogonal polynomials [25,26,27]

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Conclusion