Open AccessExistence of solutions for fractional differential equation with periodic boundary condition
Author(s) -
Xiaoxin Zuo,
AUTHOR_ID,
Weibing Wang
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022369
Subject(s) - mathematics , fixed point theorem , monotone polygon , boundary value problem , mathematical analysis , function (biology) , differential equation , fixed point , geometry , evolutionary biology , biology
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.