Extremal Solutions for a Caputo-Type Fractional-Order Initial Value Problem
In this paper, we study the existence of extremal solutions for a Caputo-type fractional-order initial value problem. By using the monotone iteration technique and the upper–lower solution method, we obtain our existence theorem when the nonlinearity satisfies a reverse-type Lipschitz condition. Note that our nonlinearity depends on the unknown function and its fractional-order derivative.
Authors
- Donal O’Regan (ORCID: https://orcid.org/0000-0002-4096-1469)
- Jiafa Xu (ORCID: https://orcid.org/0000-0001-6537-4167)
- Tian Wang
- Keyu Zhang (ORCID: https://orcid.org/0000-0002-6066-9481)
Institutions
- Chongqing Normal University (CN)
- Ollscoil na Gaillimhe – University of Galway (IE)
- Qilu Normal University (CN)
Publication Details
- Journal
- Fractal and Fractional
- Published
- 2025-05-10
- DOI
- https://doi.org/10.3390/fractalfract9050308
- Primary Topic
- Fractional Differential Equations Solutions
- Type
- article
- Field-Weighted Citation Impact
- 0.00