Topology degree results on a G-ABC implicit fractional differential equation under three-point boundary conditions

Shahram Rezapour; Sabri T M Thabet; Ava Sh Rafeeq; Imed Kedim; Miguel Vivas-Cortez; Nasser Aghazadeh

doi:10.1371/journal.pone.0300590

Topology degree results on a G-ABC implicit fractional differential equation under three-point boundary conditions

PLoS One. 2024 Jul 1;19(7):e0300590. doi: 10.1371/journal.pone.0300590. eCollection 2024.

Authors

Shahram Rezapour^{1

2

3

4}, Sabri T M Thabet^{5

6

7}, Ava Sh Rafeeq⁸, Imed Kedim⁹, Miguel Vivas-Cortez¹⁰, Nasser Aghazadeh¹¹

Affiliations

¹ Institute of Research and Development, Duy Tan University, Da Nang, Vietnam.
² Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.
³ Insurance Research Center (IRC), Tehran, Iran.
⁴ Department of Medical Research, China Medical University Hospital, China Medical University,Taichung, Taiwan.
⁵ Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu, India.
⁶ Department of Mathematics, Radfan University College, University of Lahej, Lahej, Yemen.
⁷ Department of Mathematics, College of Science, Korea University, Seoul, South Korea.
⁸ Department of Mathematics, College of Science, University of Zakho, Duhok, Iraq.
⁹ Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj, Saudi Arabia.
¹⁰ Faculty of Exact and Natural Sciences, School of Physical Sciences and Mathematics, Pontifical Catholic University of Ecuador, Sede Quito, Ecuador.
¹¹ Department of Mathematics, Izmir Institute of Technology, Izmir, Türkiye.

Abstract

This research manuscript aims to study a novel implicit differential equation in the non-singular fractional derivatives sense, namely Atangana-Baleanu-Caputo ([Formula: see text]) of arbitrary orders belonging to the interval (2, 3] with respect to another positive and increasing function. The major results of the existence and uniqueness are investigated by utilizing the Banach and topology degree theorems. The stability of the Ulam-Hyers ([Formula: see text]) type is analyzed by employing the topics of nonlinear analysis. Finally, two examples are constructed and enhanced with some special cases as well as illustrative graphics for checking the influence of major outcomes.

Copyright: © 2024 Rezapour et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

MeSH terms

Algorithms*
Models, Theoretical
Nonlinear Dynamics

Grants and funding

Pontificia Universidad Cat´olica del Ecuador, Proyecto T´ıtulo: “Algunos resultados Cualitativos sobre Ecuaciones diferenciales fraccionales y desigualdades integrales” (Cod UIO2022 to M. V-C). This study is supported via funding from Prince Sattam bin Abdulaziz University project number (PSAU/2024/R/1445 to I. K.).