Author ORCID Identifier
Neugebauer, Jeffrey/0000-0003-2450-4169; Lyons, Jeffrey/0000-0003-0808-802X
Department
Mathematics and Statistics
Document Type
Article
Publication Date
4-18-2025
Abstract
This paper investigates the existence and nonexistence of positive solutions for a class of nonlinear Riemann–Liouville fractional boundary value problems of order 𝛼 +2𝑛, where 𝛼 ∈(𝑚 −1,𝑚] with 𝑚 ≥3 and 𝑚,𝑛 ∈ℕ. The conjugate fractional boundary conditions are inspired by Lidstone conditions. The nonlinearity depends on a positive parameter on which we identify constraints that determine the existence or nonexistence of positive solutions. Our method involves constructing Green’s function by convolving the Green functions of a lower-order fractional boundary value problem and a conjugate boundary value problem and using properties of this Green function to apply the Guo–Krasnosel’skii fixed-point theorem. Illustrative examples are provided to demonstrate existence and nonexistence intervals.
Recommended Citation
Lyons, Jeffrey; Neugebauer, Jeffrey T.; and Wingo, Aaron G., "Existence and Nonexistence of Positive Solutions for Fractional Boundary Value Problems with Lidstone-Inspired Fractional Conditions" (2025). EKU Faculty and Staff Scholarship. 776.
https://encompass.eku.edu/fs_research/776
Journal Title
Mathematics
