Identification of numerical solutions of a fractal-fractional divorce epidemic model of nonlinear systems via anti-divorce counseling

Maysaa Al-Qurashi; Sobia Sultana; Shazia Karim; Saima Rashid; Fahd Jarad; Mohammed Shaaf Alharthi; Maysaa Al-Qurashi; Sobia Sultana; Shazia Karim; Saima Rashid; Fahd Jarad; Mohammed Shaaf Alharthi

doi:10.3934/math.2023263

AIMS Mathematics

2023, Volume 8, Issue 3: 5233-5265. doi: 10.3934/math.2023263

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Identification of numerical solutions of a fractal-fractional divorce epidemic model of nonlinear systems via anti-divorce counseling

1.
Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
2.
Department of Mathematics, Saudi Electronic University, Riyadh, Saudi Arabia
3.
Department of Mathematics, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
4.
Department of Basic Sciences and Humanities, UET Lahore, Faisalabad Campus, Lahore, Pakistan
5.
Department of Mathematics, Government College University, Faisalabad, Pakistan
6.
Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
7.
Department of Mathematics, Çankaya University, Ankara, Turkey
8.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
9.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 26 October 2022 Revised: 26 November 2022 Accepted: 30 November 2022 Published: 14 December 2022
MSC : 46S40, 47H10, 54H25

Divorce is the dissolution of two parties' marriage. Separation and divorce are the major obstacles to the viability of a stable family dynamic. In this research, we employ a basic incidence functional as the source of interpersonal disagreement to build an epidemiological framework of divorce outbreaks via the fractal-fractional technique in the Atangana-Baleanu perspective. The research utilized Lyapunov processes to determine whether the two steady states (divorce-free and endemic steady state point) are globally asymptotically robust. Local stability and eigenvalues methodologies were used to examine local stability. The next-generation matrix approach also provides the fundamental reproducing quantity $ \bar{\mathbb{R}_{0}} $. The existence and stability of the equilibrium point can be assessed using $ \bar{\mathbb{R}}_0 $, demonstrating that counseling services for the separated are beneficial to the individuals' well-being and, as a result, the population. The fractal-fractional Atangana-Baleanu operator is applied to the divorce epidemic model, and an innovative technique is used to illustrate its mathematical interpretation. We compare the fractal-fractional model to a framework accommodating different fractal-dimensions and fractional-orders and deduce that the fractal-fractional data fits the stabilized marriages significantly and cannot break again.
- divorce epidemic model,
- fractal-fractional Atangana-Baleanu derivative operator,
- numerical solutions,
- counseling,
- stability analysis
Citation: Maysaa Al-Qurashi, Sobia Sultana, Shazia Karim, Saima Rashid, Fahd Jarad, Mohammed Shaaf Alharthi. Identification of numerical solutions of a fractal-fractional divorce epidemic model of nonlinear systems via anti-divorce counseling[J]. AIMS Mathematics, 2023, 8(3): 5233-5265. doi: 10.3934/math.2023263

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Abstract

Divorce is the dissolution of two parties' marriage. Separation and divorce are the major obstacles to the viability of a stable family dynamic. In this research, we employ a basic incidence functional as the source of interpersonal disagreement to build an epidemiological framework of divorce outbreaks via the fractal-fractional technique in the Atangana-Baleanu perspective. The research utilized Lyapunov processes to determine whether the two steady states (divorce-free and endemic steady state point) are globally asymptotically robust. Local stability and eigenvalues methodologies were used to examine local stability. The next-generation matrix approach also provides the fundamental reproducing quantity $ \bar{\mathbb{R}_{0}} $. The existence and stability of the equilibrium point can be assessed using $ \bar{\mathbb{R}}_0 $, demonstrating that counseling services for the separated are beneficial to the individuals' well-being and, as a result, the population. The fractal-fractional Atangana-Baleanu operator is applied to the divorce epidemic model, and an innovative technique is used to illustrate its mathematical interpretation. We compare the fractal-fractional model to a framework accommodating different fractal-dimensions and fractional-orders and deduce that the fractal-fractional data fits the stabilized marriages significantly and cannot break again.

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