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Article

The Existence, Uniqueness, and Multiplicity of Solutions for Two Fractional Nonlocal Equations

by
Yue Wang
1,
Wei Wei
1,2,* and
Ying Zhou
1
1
School of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
2
School of Mathematics and Big Data, Guizhou Education University, Guiyang 550018, China
*
Author to whom correspondence should be addressed.
Axioms 2023, 12(1), 45; https://doi.org/10.3390/axioms12010045
Submission received: 3 December 2022 / Revised: 22 December 2022 / Accepted: 24 December 2022 / Published: 1 January 2023
(This article belongs to the Special Issue Impulsive, Delay and Fractional Order Systems)
Versions Notes

Abstract

This paper establishes the existence of unique and multiple solutions to two nonlocal equations with fractional operators. The main results are obtained using the variational method and algebraic analysis. The conclusion is that there exists a constant λ*>0 such that the equations have only three, two, and one solution, respectively, for λ∈(0,λ*), λ=λ*, and λ>λ*. The main conclusions fill the gap in the knowledge of this kind of fractional-order problem.
Keywords: fractional nonlocal equation; variational method; algebraic analysis fractional nonlocal equation; variational method; algebraic analysis

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MDPI and ACS Style

Wang, Y.; Wei, W.; Zhou, Y. The Existence, Uniqueness, and Multiplicity of Solutions for Two Fractional Nonlocal Equations. Axioms 2023, 12, 45. https://doi.org/10.3390/axioms12010045

AMA Style

Wang Y, Wei W, Zhou Y. The Existence, Uniqueness, and Multiplicity of Solutions for Two Fractional Nonlocal Equations. Axioms. 2023; 12(1):45. https://doi.org/10.3390/axioms12010045

Chicago/Turabian Style

Wang, Yue, Wei Wei, and Ying Zhou. 2023. "The Existence, Uniqueness, and Multiplicity of Solutions for Two Fractional Nonlocal Equations" Axioms 12, no. 1: 45. https://doi.org/10.3390/axioms12010045

APA Style

Wang, Y., Wei, W., & Zhou, Y. (2023). The Existence, Uniqueness, and Multiplicity of Solutions for Two Fractional Nonlocal Equations. Axioms, 12(1), 45. https://doi.org/10.3390/axioms12010045

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