Abstract

In this paper, we study the boundary value problem of a fractional q -difference equation with nonlocal integral boundary conditions on the half-line. Using the properties of the Green function and monotone iterative method, the extremal solutions are obtained. Finally, an example is presented to illustrate our main results.

Highlights

  • We are concerned with the following fractional q-differential equation with integral boundary value problem on the half-line:

  • By applying the nonlinear alternative of Leray–Schauder type and Krasnoselskii’s fixed point theorems, the authors obtain some sufficient conditions for the existence of positive solutions to the considered problem

  • Our main purpose of this paper is by constructing a suitable Banach space, defining appropriate operators, and using the monotone iterative method, which is different from the method in [17] to obtain the existence and uniqueness of positive solutions

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Summary

Introduction

We are concerned with the following fractional q-differential equation with integral boundary value problem on the half-line:. By applying the nonlinear alternative of Leray–Schauder type and Krasnoselskii’s fixed point theorems, the authors obtain some sufficient conditions for the existence of positive solutions to the considered problem. In [17], the authors investigate the existence of solutions for the following boundary value problem of nonlinear fractional q-difference equations on the half-line. To the best of our knowledge, there are few papers that consider the boundary value of nonlinear fractional q-difference equations with nonlocal conditions on the half-line, the study of such problems is very important. Our main purpose of this paper is by constructing a suitable Banach space, defining appropriate operators, and using the monotone iterative method, which is different from the method in [17] to obtain the existence and uniqueness of positive solutions

Preliminaries on q-Calculus and Lemmas
Main Results
Example
Conclusions
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