Correction: Kiskinov et al. Existence of Absolutely Continuous Fundamental Matrix of Linear Fractional System with Distributed Delays. Mathematics 2021, 9, 150

Hristo Kiskinov; Ekaterina Madamlieva; Magdalena Veselinova; Andrey Zahariev

doi:10.3390/math9111282

,

and

Faculty of Mathematics and Informatics, University of Plovdiv, 4000 Plovdiv, Bulgaria

^*

Author to whom correspondence should be addressed.

Mathematics2021, 9(11), 1282;https://doi.org/10.3390/math9111282

Version Notes

Order Reprints

We have found that, in the right side of Equation (35) in our paper [1], the addend

T_{a - h} (t, a - h) Φ (a - h)

is missing. As consequence of this error, the same addend must also be added in the right side of Equations (38), (39), (41) and (42).

The correct Equations (35), (38), (39), (41) and (42) are listed below:

X_{Φ} (t) = \int_{a - h}^{a} T_{a - h} (t, s) d_{s} Φ (s) + T_{a - h} (t, a - h) Φ (a - h), t \in J_{a}

(35)

X_{f}^{Φ} (t) = X_{Φ} (t) + X_{f} (t) = \int_{a}^{t} C {(t, s)}_{R L} D_{a +}^{1 - α} F (s) d s + \int_{a - h}^{a} T_{a - h} (t, s) d_{s} Φ (s) + T_{a - h} (t, a - h) Φ (a - h)

(38)

\begin{matrix} X_{f}^{Φ} (t) & = T_{a - h} (t, a) (Φ_{J} (a +) - Φ_{J} (a -)) + \sum_{i} T_{a - h} (t, s_{i}) ((Φ_{J} (s_{i} +) - Φ_{J} (s_{i} -)) \\ + \int_{a - h}^{a} T_{a - h} (t, s) Φ_{A}^{^{'}} (s) d s + \int_{a}^{t} C {(t, s)}_{R L} D_{a +}^{1 - α} F (s) d s + T_{a - h} (t, a - h) Φ (a - h) \end{matrix}

(39)

X_{Φ} (t) = T_{a - h} (t, a) Φ_{J} (a +) - \int_{a - h}^{a} \frac{\partial T_{a - h} (t, s)}{\partial s} Φ_{A} (s) d s + T_{a - h} (t, a - h) Φ (a - h)

(41)

\begin{matrix} X_{Φ} (t) & = T_{a - h} (t, a) (Φ_{J} (a +) - Φ_{J} (a -)) \\ + \sum_{i} T_{a - h} (t, s_{i}) (Φ_{J} (s_{i} +) - Φ_{J} (s_{i} -)) + \int_{a - h}^{a} T_{a - h} (t, s) Φ_{A}^{^{'}} (s) d s + T_{a - h} (t, a - h) Φ (a - h) \end{matrix}

(42)

The authors apologize for any inconvenience caused and state that the scientific conclusions are unaffected. The original article has been updated.

Author Contributions

Conceptualization, H.K., E.M., M.V. and A.Z. Writing—Review and Editing, H.K., E.M., M.V. and A.Z. All authors contribution in the article are equal. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Reference

Kiskinov, H.; Madamlieva, E.; Veselinova, M.; Zahariev, A. Existence of absolutely continuous fundamental matrix of linear fractional system with distributed delays. Mathematics 2021, 9, 150. [Google Scholar] [CrossRef]

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).