2011.03999
A natural extension of Mittag-Leffler function associated with a triple infinite series
Ismail T. Huseynov, Arzu Ahmadova, Gbenga O. Ojo, Nazim I. Mahmudov
correctmedium confidence
- Category
- math.DS
- Journal tier
- Specialist/Solid
- Processed
- Sep 28, 2025, 12:55 AM
- arXiv Links
- Abstract ↗PDF ↗
Audit review
The paper and the model produce the same explicit solution for the three‑order Caputo FDE, including the homogeneous series and the inhomogeneous convolution kernel, and they agree with the equation as posed in the paper. The paper argues via Laplace transform and a convolution identity, while the model uses a Volterra/Neumann‑series approach. Both slightly overstate C1-regularity for 0<α<1, but the main formulae and verification are consistent.
Referee report (LaTeX)
\textbf{Recommendation:} minor revisions
\textbf{Journal Tier:} specialist/solid
\textbf{Justification:}
The paper proposes a clear trivariate Mittag–Leffler framework and applies it to multi-term Caputo equations, yielding explicit homogeneous and inhomogeneous solutions that align with established Fox–Wright approaches. The main identities appear correct and useful. However, a key theorem in the inhomogeneous case is stated without proof, some term-by-term operations lack convergence justification, and the C1 regularity claim is stronger than generally valid for 0<α<1. Addressing these will improve rigor without changing the principal contributions.