Mathematicians Prove When Fractional Boundary Value Problems Have Unique Positive Solutions

A new study in the journal Boundary Value Problems establishes rigorous conditions under which a class of singular nonlinear fractional differential equations admits positive solutions, and when those solutions are unique. The paper, authored by Fulin Wu and Qinrui Shen, was published on 27 October 2026 as an open access research article.

The equations examined carry Riemann-Stieltjes integral boundary conditions and involve Riemann-Liouville fractional derivatives.

Uniqueness is then obtained through a different route: the Banach contraction mapping principle, which guarantees a single fixed point when the operator is contractive. The paper also establishes local Ulam-Hyers stability of the equation, showing that for sufficiently small perturbations the solutions remain stable in a precise mathematical sense.

According to the abstract, the results generalize related conclusions in the existing literature on fractional boundary value problems. Because the article is being shared early as peer-reviewed, accepted research, it is citable and carries a permanent DOI, though the published version remains subject to further edits before the final Version of Record replaces it.

Subject of Research: Existence and uniqueness of positive solutions for fractional differential equations with integral boundary conditions

Article Title: Existence and uniqueness of positive solutions for integral boundary value problems of fractional differential equations

Article References: Wu, F., & Shen, Q. (2026). Existence and uniqueness of positive solutions for integral boundary value problems of fractional differential equations. Boundary Value Problems. https://doi.org/10.1186/s13661-026-02380-z

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DOI: 10.1186/s13661-026-02380-z

Keywords: fractional differential equations, boundary value problems, positive solutions, Riemann-Liouville derivatives, fixed point theorem, Banach contraction principle, Ulam-Hyers stability, integral boundary conditions, nonlinear analysis, Existence, uniqueness, positive