Nontrivial solutions for a fractional differential equation with nonlocal Riemann-Stieltjes boundary conditions

Volume 10, Issue 11, pp 6042--6055 http://dx.doi.org/10.22436/jnsa.010.11.39

Publication Date: November 26, 2017 Submission Date: August 11, 2017

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Authors

Xinguang Zhang - School of Mathematical and Informational Sciences, Yantai University, Yantai 264005, Shandong, China. - Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia. Lishan Liu - School of Mathematical Sciences, Qufu Normal University, Qufu 273165, Shandong, China. - Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia. Yonghong Wu - Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845, Australia. Yujun Cui - Department of Mathematics, Shandong University of Science and Technology, Qingdao, 266590, Shandong, China.

Abstract

The model of fractional differential equation arises from various fields of physics, engineering, and applied mathematics. In this paper, we focus on the existence and uniqueness of nontrivial solutions for a abstract model of fractional differential equation with nonlocal Riemann-Stieltjes boundary conditions. Under certain suitable growth conditions, we establish some sufficient conditions for the existence and uniqueness of nontrivial solutions based on Leray-Schauder nonlinear alternative and Schauder fixed point theorem.

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Keywords

• Fractional differential equation
• nontrivial solution
• nonlocal Riemann-Stieltjes boundary conditions
• fixed point theorem

MSC

•  34B15
•  34B18

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