Generalized existence and uniqueness results for nonlinear Caputo fractional boundary value problems
Abstract
In this paper, we study a class of nonlinear fractional boundary value problems involving the Caputo fractional derivative of order $ \tau \in (1, 2] $. We establish sufficient conditions for the existence and uniqueness of solutions. Our analysis is based on Krasnoselskii's fixed-point theorem and the Banach contraction principle in appropriate Banach spaces. The obtained results not only guarantee the solvability of the proposed equation but also generalize and improve several related results available in the literature. An example is provided in several orders to validate the results.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Fractional Differential Equations Solutions
Fixed Point Theorems Analysis
Publication details
- Journal / source
- AIMS Mathematics
- Publisher
- American Institute of Mathematical Sciences (AIMS)
- Volume
- 11
- Issue
- 2
- Pages
- 4586–4595
- Publication date
- 1 January 2026