On uniform stability and numerical simulations of complex valued neural networks involving generalized Caputo fractional order

Sumati Kumari Panda; Thabet Abdeljawad; A M Nagy

doi:10.1038/s41598-024-53670-4

On uniform stability and numerical simulations of complex valued neural networks involving generalized Caputo fractional order

Sci Rep. 2024 Feb 19;14(1):4073. doi: 10.1038/s41598-024-53670-4.

Authors

Sumati Kumari Panda^#¹, Thabet Abdeljawad^#^{2

3

4}, A M Nagy^#^{5

6}

Affiliations

¹ Department of Mathematics, GMR Institute of Technology, Rajam, Andhra Pradesh, 532127, India.
² Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia. tabdeljawad@psu.edu.sa.
³ Department of Medical Research, China Medical University, Taichung, 40402, Taiwan. tabdeljawad@psu.edu.sa.
⁴ Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Garankuwa, Medusa, 0204, South Africa. tabdeljawad@psu.edu.sa.
⁵ Department of Mathematics, College of Science, Kuwait University, 13060, Safat, Kuwait.
⁶ Department of Mathematics, Faculty of Science, Benha University, Benha, 13518, Egypt.

^# Contributed equally.

PMID: 38374277
DOI: 10.1038/s41598-024-53670-4

Abstract

The dynamics and existence results of generalized Caputo fractional derivatives have been studied by several authors. Uniform stability and equilibrium in fractional-order neural networks with generalized Caputo derivatives in real-valued settings, however, have not been extensively studied. In contrast to earlier studies, we first investigate the uniform stability and equilibrium results for complex-valued neural networks within the framework of a generalized Caputo fractional derivative. We investigate the intermittent behavior of complex-valued neural networks in generalized Caputo fractional-order contexts. Numerical results are supplied to demonstrate the viability and accuracy of the presented results. At the end of the article, a few open questions are posed.