The Solution of Modified Fractional Bergman’s Minimal Blood Glucose-Insulin Model

Alkahtani, Badr Saad T.; Algahtani, Obaid; Dubey, Ravi Shanker; Goswami, Pranay

doi:10.3390/e19050114

Cited by 23 publications

(14 citation statements)

References 12 publications

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“…In [17], the authors obtained analytical solutions for the fractional Bergman's minimal model involving the Adomian decomposition method. Alkahtani in [1] solved the fractional Bergman's minimal model using the Caputo-Fabrizio fractional-order derivative. The existence and uniqueness of the solution were discussed.…”

Section: Morales-delgado Gómez-aguilar and Taneco-hernándezmentioning

confidence: 99%

Mathematical modeling approach to the fractional Bergman's model

Morales‐Delgado¹,

Gómez‐Aguilar²,

Taneco-Hernández³

2020

Discrete &Amp; Continuous Dynamical Systems - S

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This paper presents the solution for a fractional Bergman's minimal blood glucose-insulin model expressed by Atangana-Baleanu-Caputo fractional order derivative and fractional conformable derivative in Liouville-Caputo sense. Applying homotopy analysis method and Laplace transform with homotopy polynomial we obtain analytical approximate solutions for both derivatives. Finally, some numerical simulations are carried out for illustrating the results obtained. In addition, the calculations involved in the modified homotopy analysis transform method are simple and straightforward.

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Section: Morales-delgado Gómez-aguilar and Taneco-hernándezmentioning

confidence: 99%

Mathematical modeling approach to the fractional Bergman's model

Morales‐Delgado¹,

Gómez‐Aguilar²,

Taneco-Hernández³

2020

Discrete &Amp; Continuous Dynamical Systems - S

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“…Uniqueness of the coupled solutions. In this section, we show that the solutions of equation (10) and (11) are unique. To prove the uniqueness, we have considered that there is an another solution for equation (10), then…”

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confidence: 95%

“…To define the existence of the coupled solution we use the Fixed-Point theorem. In this way first we transform the equations (10) and (11) in to integral equation as follows…”

mentioning

confidence: 99%

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Mathematical model of diabetes and its complication involving fractional operator without singular kernal

Dubey¹,

Goswami²

2021

DCDS-S

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Diabetes is one of the burning issues of the whole world. It effected the world population rapidly. According to the WHO approx 415 million people are living with diabetes in the world and this figure is expected to rise up to 642 million by 2040. World various organizations raise their voice against the dire facts about the increasing graph of diabetes and its complicated patients. In this paper authors define the fractional model of diabetes and its complications involving to fractional operator with exponential kernel. The authors discuss the existence of the solution by using fixed point theorem and also show the uniqueness of the solution. To validate the model's efficiency the authors provided numerical simulation by using HPM. To strengthen the model the results have been presented in the form of graphs.

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“…On the other hand, Casson fluid has been modeled in [52]. In [12], Bergman minimal blood glucose-insulin model has been generalized. The CF operator has also been used to investigate the motion of a charged field [44].…”

mentioning

confidence: 99%

New aspects of time fractional optimal control problems within operators with nonsingular kernel

Yıldız¹,

Jajarmi²,

Yıldız³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - S

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This paper deals with a new formulation of time fractional optimal control problems governed by Caputo-Fabrizio (CF) fractional derivative. The optimality system for this problem is derived, which contains the forward and backward fractional differential equations in the sense of CF. These equations are then expressed in terms of Volterra integrals and also solved by a new numerical scheme based on approximating the Volterra integrals. The linear rate of convergence for this method is also justified theoretically. We present three illustrative examples to show the performance of this method. These examples also test the contribution of using CF derivative for dynamical constraints and we observe the efficiency of this new approach compared to the classical version of fractional operators.

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The Solution of Modified Fractional Bergman’s Minimal Blood Glucose-Insulin Model

Cited by 23 publications

References 12 publications

Mathematical modeling approach to the fractional Bergman's model

Mathematical modeling approach to the fractional Bergman's model

Mathematical model of diabetes and its complication involving fractional operator without singular kernal

New aspects of time fractional optimal control problems within operators with nonsingular kernel

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