Approximate numerical algorithms and artificial neural networks for analyzing a fractal-fractional mathematical model

Hashem Najafi; Abdallah Bensayah; Brahim Tellab; Sina Etemad; Sotiris K. Ntouyas; Shahram Rezapour; Jessada Tariboon; Hashem Najafi; Abdallah Bensayah; Brahim Tellab; Sina Etemad; Sotiris K. Ntouyas; Shahram Rezapour; Jessada Tariboon

doi:10.3934/math.20231447

AIMS Mathematics

2023, Volume 8, Issue 12: 28280-28307. doi: 10.3934/math.20231447

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Research article

Approximate numerical algorithms and artificial neural networks for analyzing a fractal-fractional mathematical model

1.
Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran
2.
Laboratoire de Mathématiques Appliquées, Université Kasdi Merbah, Ouargla 30000, Algeria
3.
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran
4.
Department of Mathematics, University of Ioannina, Ioannina 451 10, Greece
5.
Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
6.
Department of Mathematics, Kyung Hee University, 26 Kyungheedae-ro, Dongdaemun-gu, Seoul, Republic of Korea
7.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
8.
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand

Received: 16 August 2023 Revised: 07 October 2023 Accepted: 09 October 2023 Published: 16 October 2023
MSC : 26A33, 34A08, 35R11

In this paper, an analysis of a mathematical model of the coronavirus is carried out by using two fractal-fractional parameters. This dangerous virus infects a person through the mouth, eyes, nose or hands. This makes it so dangerous that no one can get rid of it. One of the main factors contributing to increasing infections of this deadly virus is crowding. We believe that it is necessary to model this effect mathematically to predict the possible outcomes. Hence, the study of neural network-based models related to the spread of this virus can yield new results. This paper also introduces the use of artificial neural networks (ANNs) to approximate the solutions, which is a significant contribution in this regard. We suggest employing this new method to solve a system of integral equations that explain the dynamics of infectious diseases instead of the classical numerical methods. Our study shows that, compared to the Adams-Bashforth algorithm, the ANN is a reliable candidate for solving the problems.
- fractal-fractional derivative,
- fixed-point theorem,
- artificial neural networks
Citation: Hashem Najafi, Abdallah Bensayah, Brahim Tellab, Sina Etemad, Sotiris K. Ntouyas, Shahram Rezapour, Jessada Tariboon. Approximate numerical algorithms and artificial neural networks for analyzing a fractal-fractional mathematical model[J]. AIMS Mathematics, 2023, 8(12): 28280-28307. doi: 10.3934/math.20231447

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Abstract

In this paper, an analysis of a mathematical model of the coronavirus is carried out by using two fractal-fractional parameters. This dangerous virus infects a person through the mouth, eyes, nose or hands. This makes it so dangerous that no one can get rid of it. One of the main factors contributing to increasing infections of this deadly virus is crowding. We believe that it is necessary to model this effect mathematically to predict the possible outcomes. Hence, the study of neural network-based models related to the spread of this virus can yield new results. This paper also introduces the use of artificial neural networks (ANNs) to approximate the solutions, which is a significant contribution in this regard. We suggest employing this new method to solve a system of integral equations that explain the dynamics of infectious diseases instead of the classical numerical methods. Our study shows that, compared to the Adams-Bashforth algorithm, the ANN is a reliable candidate for solving the problems.

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