Existence of solutions for fractional differential equation with periodic boundary condition

Xiaoxin Zuo; Weibing Wang; Xiaoxin Zuo; Weibing Wang

doi:10.3934/math.2022369

AIMS Mathematics

2022, Volume 7, Issue 4: 6619-6633. doi: 10.3934/math.2022369

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Research article

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

Received: 03 December 2021 Revised: 20 January 2022 Accepted: 20 January 2022 Published: 21 January 2022
MSC : 34A08, 34A12

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.
- Caputo fractional differential equation,
- periodic boundary condition,
- Krasnosel'skii fixed point theorem,
- monotone iterative method,
- Green's function
Citation: Xiaoxin Zuo, Weibing Wang. Existence of solutions for fractional differential equation with periodic boundary condition[J]. AIMS Mathematics, 2022, 7(4): 6619-6633. doi: 10.3934/math.2022369

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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.

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