Positive Solutions of a Riemann-Liouville Fractional Dirichlet Boundary Value Problem: Existence, Uniqueness, and Parameter Dependence
DOI:
https://doi.org/10.15377/2409-5761.2026.13.10Keywords:
Positive solutions, Parameter dependence, Existence and uniqueness, Dirichlet boundary value problem, Riemann-liouville fractional derivativeAbstract
In this article, we discuss the parameter dependence of positive solutions to fractional differential equations with Dirichlet boundary value conditions. Through fixed point theorems about increasing operators and decreasing operators, the existence and uniqueness of positive solutions is proved for each given fixed positive parameter. We analyze the monotonicity, continuity and limit behavior of solutions with respect to the parameter, and an iterative sequence is established to approximate this unique solution. Finally, we give two examples which prove the applicability and validity of the main conclusion.
2020 MR Subject Classification 26A33; 34B15; 34B18.
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