Novel analysis of nonlinear dynamics of a fractional model for tuberculosis disease via the generalized Caputo fractional derivative operator (case study of Nigeria)

Saima Rashid; Yolanda Guerrero Sánchez; Jagdev Singh; Khadijah M Abualnaja; Saima Rashid; Yolanda Guerrero Sánchez; Jagdev Singh; Khadijah M Abualnaja

doi:10.3934/math.2022562

AIMS Mathematics

2022, Volume 7, Issue 6: 10096-10121. doi: 10.3934/math.2022562

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Novel analysis of nonlinear dynamics of a fractional model for tuberculosis disease via the generalized Caputo fractional derivative operator (case study of Nigeria)

1.
Department of Mathematics, Government College University, Faisalabad, Pakistan
2.
Departamento de Anatomía y Psicobiología, Universidad de Murcia, 30100-Murcia
3.
Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India
4.
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 08 December 2021 Revised: 02 March 2022 Accepted: 07 March 2022 Published: 21 March 2022
MSC : 46S40, 47H10, 54H25

We propose a new mathematical framework of generalized fractional-order to investigate the tuberculosis model with treatment. Under the generalized Caputo fractional derivative notion, the system comprises a network of five nonlinear differential equations. Besides that, the equilibrium points, stability and basic reproductive number are calculated. The concerned derivative involves a power-law kernel and, very recently, it has been adapted for various applied problems. The existence findings for the fractional-order tuberculosis model are validated using the Banach and Leray-Schauder nonlinear alternative fixed point postulates. For the developed framework, we have generated various forms of Ulam's stability outcomes. To investigate the estimated response and nonlinear behaviour of the system under investigation, the efficient mathematical formulation known as the $ \wp $-Laplace Adomian decomposition technique algorithm was implemented. It is important to mention that, with the exception of numerous contemporary discussions, spatial coherence was considered throughout the fractionalization procedure of the classical model. Simulation and comparison analysis yield more versatile outcomes than the existing techniques.
- $ \wp $-Laplace transform,
- generalized Caputo fractional derivative,
- Leray-Schauder fixed point theorem,
- Ulam's stability
Citation: Saima Rashid, Yolanda Guerrero Sánchez, Jagdev Singh, Khadijah M Abualnaja. Novel analysis of nonlinear dynamics of a fractional model for tuberculosis disease via the generalized Caputo fractional derivative operator (case study of Nigeria)[J]. AIMS Mathematics, 2022, 7(6): 10096-10121. doi: 10.3934/math.2022562

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Abstract

We propose a new mathematical framework of generalized fractional-order to investigate the tuberculosis model with treatment. Under the generalized Caputo fractional derivative notion, the system comprises a network of five nonlinear differential equations. Besides that, the equilibrium points, stability and basic reproductive number are calculated. The concerned derivative involves a power-law kernel and, very recently, it has been adapted for various applied problems. The existence findings for the fractional-order tuberculosis model are validated using the Banach and Leray-Schauder nonlinear alternative fixed point postulates. For the developed framework, we have generated various forms of Ulam's stability outcomes. To investigate the estimated response and nonlinear behaviour of the system under investigation, the efficient mathematical formulation known as the $ \wp $-Laplace Adomian decomposition technique algorithm was implemented. It is important to mention that, with the exception of numerous contemporary discussions, spatial coherence was considered throughout the fractionalization procedure of the classical model. Simulation and comparison analysis yield more versatile outcomes than the existing techniques.

References

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