Unique positive solutions for boundary value problem of p-Laplacian fractional differential equation with a sign-changed nonlinearity
Articles
Wenxia Wang
Taiyuan Normal University
https://orcid.org/0000-0001-8064-1446
Published 2022-10-19
https://doi.org/10.15388/namc.2022.27.29503
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Keywords

fractional boundary value problem
p-Laplacian operator
positive solution
fixed point theorem of sum operator
Mittag-Leffler function

How to Cite

Wang, W. (2022) “Unique positive solutions for boundary value problem of p-Laplacian fractional differential equation with a sign-changed nonlinearity”, Nonlinear Analysis: Modelling and Control, 27(6), pp. 1110–1128. doi:10.15388/namc.2022.27.29503.

Abstract

This paper investigates the existence of a unique positive solution for a class of boundary value problems of p-Laplacian fractional differential equations, where its nonlinearity is signchanged and involves a fractional derivative term, and its boundary involves a nonlinear fractional integral term. By constructing an appropriate auxiliary boundary value problem and applying a generalized fixed point theorem of sum operator and properties of Mittag-Leffler function, some sufficient conditions for the existence of a unique positive solution are presented, and a monotone iterative sequence uniformly converging to the unique solution is constructed. In addition, an example is given to illustrate the main result.

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