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Research Article | Open Access

Existence of solutions for fractional differential equation with periodic boundary condition

Xiaoxin Zuo( ), Weibing Wang
Department of Mathematics, Hunan Unviersity of Science and Technology, Xiangtan, Hunan, China
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Abstract

We investigate the existence of solutions for a Caputo fractional differential equation with periodic boundary condition. Using the positivity of Green's function of the corresponding linear equation, we show the existence of positive solutions by using Krasnosel'skii fixed point theorem. Meanwhile, by using monotone iterative method and lower and upper solutions method, we also discuss the existence of extremal solutions for a special case.

Keywords

Caputo fractional differential equationperiodic boundary conditionKrasnosel'skii fixed point theoremmonotone iterative methodGreen's function
CLC number: 34A08, 34A12

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 6619-6633
DOI: 10.3934/math.2022369

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Cite this article:
Zuo X, Wang W. Existence of solutions for fractional differential equation with periodic boundary condition. AIMS Mathematics, 2022, 7(4): 6619-6633. https://doi.org/10.3934/math.2022369

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Received: 03 December 2021
Revised: 20 January 2022
Accepted: 20 January 2022
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)