A study of behaviour for fractional order diabetes model via the nonsingular kernel

Saima Rashid; Fahd Jarad; Taghreed M. Jawa; Saima Rashid; Fahd Jarad; Taghreed M. Jawa

doi:10.3934/math.2022282

AIMS Mathematics

2022, Volume 7, Issue 4: 5072-5092. doi: 10.3934/math.2022282

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A study of behaviour for fractional order diabetes model via the nonsingular kernel

1.
Department of Mathematics, Government College University, Faisalabad, Pakistan
2.
Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey
3.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4.
Department of Mathematics and Statistics, College of Sciences, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Received: 18 November 2021 Revised: 21 December 2021 Accepted: 23 December 2021 Published: 29 December 2021
MSC : 46S40, 47H10, 54H25

A susceptible diabetes comorbidity model was used in the mathematical treatment to explain the predominance of mellitus. In the susceptible diabetes comorbidity model, diabetic patients were divided into three groups: susceptible diabetes, uncomplicated diabetics, and complicated diabetics. In this research, we investigate the susceptible diabetes comorbidity model and its intricacy via the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). The analysis backs up the idea that the aforesaid fractional order technique plays an important role in predicting whether or not a person will develop diabetes after a substantial immunological assault. Using the fixed point postulates, several theoretic outcomes of existence and Ulam's stability are proposed for the susceptible diabetes comorbidity model. Meanwhile, a mathematical approach is provided for determining the numerical solution of the developed framework employing the Adams type predictor–corrector algorithm for the ABC-fractional integral operator. Numerous mathematical representations correlating to multiple fractional orders are shown. It brings up the prospect of employing this structure to generate framework regulators for glucose metabolism in type 2 diabetes mellitus patients.
- fractional diabetes model,
- Atangana-Baleanu fractional derivative operator,
- fixed point theory,
- Ulam's stability,
- Adams type predictor–corrector method
Citation: Saima Rashid, Fahd Jarad, Taghreed M. Jawa. A study of behaviour for fractional order diabetes model via the nonsingular kernel[J]. AIMS Mathematics, 2022, 7(4): 5072-5092. doi: 10.3934/math.2022282

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Abstract

A susceptible diabetes comorbidity model was used in the mathematical treatment to explain the predominance of mellitus. In the susceptible diabetes comorbidity model, diabetic patients were divided into three groups: susceptible diabetes, uncomplicated diabetics, and complicated diabetics. In this research, we investigate the susceptible diabetes comorbidity model and its intricacy via the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). The analysis backs up the idea that the aforesaid fractional order technique plays an important role in predicting whether or not a person will develop diabetes after a substantial immunological assault. Using the fixed point postulates, several theoretic outcomes of existence and Ulam's stability are proposed for the susceptible diabetes comorbidity model. Meanwhile, a mathematical approach is provided for determining the numerical solution of the developed framework employing the Adams type predictor–corrector algorithm for the ABC-fractional integral operator. Numerous mathematical representations correlating to multiple fractional orders are shown. It brings up the prospect of employing this structure to generate framework regulators for glucose metabolism in type 2 diabetes mellitus patients.

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