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Peer-reviewedCC BY 4.0Mathematics

On a Nonlinear Fractional Delay Differential Equation with Nonlocal Boundary Conditions

  • Chenkuan Li1
  • Wenyuan Liao2
  • Jianfei Huang3
  • Min-Jie Luo4
4 affiliations
  1. 1Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada
  2. 2Department of Mathematics and Statistics, University of Calgary, Calgary, AB T2N 1N4, Canada
  3. 3College of Mathematical Sciences, Yangzhou University, Yangzhou 225002, China
  4. 4School of Mathematics and Statistics, Donghua University, Shanghai 201620, China
Open at sourceDOICite

Abstract

The aim of this paper is to investigate the existence, uniqueness, and Hyers–Ulam stability of solutions to a class of nonlinear Caputo fractional delay differential equation with nonlocal boundary conditions in the space of absolutely continuous functions. Owing to the nonlinearity, the equation is not readily amenable to treatment using existing integral transform methods. Our approach employs the inverse operator technique, the multivariate Mittag-Leffler function, and several well-established fixed-point theorems. An illustrative example is provided to demonstrate the applicability of the obtained conditions. A heuristic discussion of an exact solution, together with sufficient conditions justifying the convergence of the associated formal series in the Laplace-transform domain, is also presented.

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Cite

BibTeXRIS
BibTeX
@article{li2026nonlinear,
  title = {{On a Nonlinear Fractional Delay Differential Equation with Nonlocal Boundary Conditions}},
  author = {Chenkuan Li and Wenyuan Liao and Jianfei Huang and Min-Jie Luo},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14193610},
  url = {https://www.mdpi.com/2227-7390/14/19/3610},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - On a Nonlinear Fractional Delay Differential Equation with Nonlocal Boundary Conditions
AU  - Chenkuan Li
AU  - Wenyuan Liao
AU  - Jianfei Huang
AU  - Min-Jie Luo
PY  - 2026
DA  - 2026/10/05
JO  - Mathematics
DO  - 10.3390/math14193610
UR  - https://www.mdpi.com/2227-7390/14/19/3610
AB  - The aim of this paper is to investigate the existence, uniqueness, and Hyers–Ulam stability of solutions to a class of nonlinear Caputo fractional delay differential equation with nonlocal boundary conditions in the space of absolutely continuous functions. Owing to the nonlinearity, the equation is not readily amenable to treatment using existing integral transform methods. Our approach employs the inverse operator technique, the multivariate Mittag-Leffler function, and several well-established fixed-point theorems. An illustrative example is provided to demonstrate the applicability of the obtained conditions. A heuristic discussion of an exact solution, together with sufficient conditions justifying the convergence of the associated formal series in the Laplace-transform domain, is also presented.
SN  - 2227-7390
ER  -