Three-Point Boundary Value Problems of Coupled Nonlocal Laplacian Equations

Huizhen Qu, Jianwen Zhou and Tianwei Zhang
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Huizhen Qu: Department of Mathematics, Yunnan University, Kunming 650091, China
Jianwen Zhou: Department of Mathematics, Yunnan University, Kunming 650091, China
Tianwei Zhang: Department of Mathematics, Yunnan University, Kunming 650091, China

Mathematics, 2022, vol. 10, issue 13, 1-18

Abstract: This paper discusses a kind of coupled nonlocal Laplacian evolution equation with Caputo time-fractional derivatives and proportional delays. Green function and mild solution are firstly established by employing the approach of eigenvalues’ expansions and Fourier analysis technique. By the properties of eigenvalues and Mittag–Leffler functions, several vital estimations of Green functions are presented. In view of these estimations and some appropriate assumptions, the existence and uniqueness of the mild solution are studied by utilizing the Leray–Schauder fixed-point theorem and the Banach fixed-point theorem. Finally, an example is provided to illustrate the effectiveness of our main results.

Keywords: nonlocal Laplace; coupled system; green function; eigenvalues’ expansion; Fourier (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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