Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval

Zheng, Yanping; Yang, Hui; Wang, Wenxia

doi:10.3390/math12020325

Open AccessArticle

Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval

by

Yanping Zheng

^*,

Hui Yang

and

Wenxia Wang

School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619, China

^*

Author to whom correspondence should be addressed.

Mathematics 2024, 12(2), 325; https://doi.org/10.3390/math12020325

Submission received: 27 November 2023 / Revised: 13 January 2024 / Accepted: 15 January 2024 / Published: 19 January 2024

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Abstract

This paper is concerned with the existence and multiplicity of monotone positive solutions for a class of nonlinear fractional differential equation with a disturbance parameter in the integral boundary conditions on the infinite interval. By using Guo–Krasnosel’skii fixed-point theorem and the analytic technique, we divide the range of parameter for the existence of at least two, one and no positive solutions for the problem. In the end, an example is given to illustrate our main results.

Keywords: boundary value problem; disturbance parameter; infinite interval; monotone positive solution

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MDPI and ACS Style

Zheng, Y.; Yang, H.; Wang, W. Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval. Mathematics 2024, 12, 325. https://doi.org/10.3390/math12020325

AMA Style

Zheng Y, Yang H, Wang W. Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval. Mathematics. 2024; 12(2):325. https://doi.org/10.3390/math12020325

Chicago/Turabian Style

Zheng, Yanping, Hui Yang, and Wenxia Wang. 2024. "Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval" Mathematics 12, no. 2: 325. https://doi.org/10.3390/math12020325

APA Style

Zheng, Y., Yang, H., & Wang, W. (2024). Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval. Mathematics, 12(2), 325. https://doi.org/10.3390/math12020325

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Monotone Positive Solutions for Nonlinear Fractional Differential Equations with a Disturbance Parameter on the Infinite Interval

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