Study of Bergman’s minimal blood glucose-insulin model by adomian decomposition method

Jain, Rinku; Arekar, Kirti; Dubey, Ravi Shanker

doi:10.1080/02522667.2016.1187919

Cited by 14 publications

(7 citation statements)

References 18 publications

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“…The solution of Equation (15) coincides with the solution obtained with the application of the conformable derivative (1). Expansion of the conformable fractional derivative in the Liouville-Caputo sense of order = 1− , with ≤ 1.…”

Section: Basic Definitions and Fractional Conformable Decomposition Msupporting

confidence: 66%

“…Many dynamic systems can be described by means of fractional derivatives. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] Fractional-order differential equations have been developed by using different computational approaches and asymptotics expansions or perturbation methods such as the Adomian decomposition method, [15][16][17] Aboodh decomposition method, 18 homotopy perturbation method, 19,20 fractional natural decomposition method, 21 Chebyshev wavelet method, 22 Laplace Adomian decomposition method, 23,24 Bernstein operational matrix method, 25,26 and q-homotopy analysis transform method. 27,28 Chaos theory is a branch of mathematics with several applications in physics, engineering, economics, and biology.…”

Section: Introductionmentioning

confidence: 99%

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Fractional conformable attractors with low fractality

Morales‐Delgado

Gómez‐Aguilar

Escobar-Jiménez

2018

Math Methods in App Sciences

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In this paper, we considered a fractional conformable derivative of Liouville-Caputo type of fractional-order = n − , which contains a small perturbation and positive integer n values between [0;1] to obtain the solutions of three different fractional conformable attractors (Chen's attractor, Genesio-Tesi's attractor, and Liu's attractor). The fractional conformable Adomian decomposition method is applied to obtain an expansion of the fractional conformable derivative in = n − . The solutions of the fractional chaotic systems are calculated in the form of convergent series. We investigate the dynamics of these attractors by numerical simulations for different fractional orders values and parameter . KEYWORDSadomian decomposition method, chaos, fractional calculus, fractional conformable derivative, low-fractality 6378

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Section: Basic Definitions and Fractional Conformable Decomposition Msupporting

confidence: 66%

Section: Introductionmentioning

confidence: 99%

Fractional conformable attractors with low fractality

Morales‐Delgado

Gómez‐Aguilar

Escobar-Jiménez

2018

Math Methods in App Sciences

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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.…”

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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“…Many powerful methods for finding exact solutions for these models have been found. [42][43][44][45][46][47][48][49] The homotopy analysis method (HAM), proposed by Liao, has been successfully applied to solving many problems in physics and engineering. [50][51][52][53] The HAM is based on construction of a homotopy that continuously deforms an initial guess approximation to the exact solution of the given problem.…”

Section: Introductionmentioning

confidence: 99%

Application of the Caputo‐Fabrizio and Atangana‐Baleanu fractional derivatives to mathematical model of cancer chemotherapy effect

Morales‐Delgado

Gómez-Aguilar

Saad

et al. 2019

Math Methods in App Sciences

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In this paper, we obtain approximate‐analytical solutions of a cancer chemotherapy effect model involving fractional derivatives with exponential kernel and with general Mittag‐Leffler function. Laplace homotopy perturbation method and the modified homotopy analysis transform method were applied. The first method is based on a combination of the Laplace transform and homotopy methods, while the second method is an analytical technique based on homotopy polynomial. The cancer chemotherapy effect equations are solved numerically and analytically using the aforesaid methods. Illustrative examples are included to demonstrate the validity and applicability of the presented technique with new fractional‐order derivatives with exponential decay law and with general Mittag‐Leffler law.

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Study of Bergman’s minimal blood glucose-insulin model by adomian decomposition method

Cited by 14 publications

References 18 publications

Fractional conformable attractors with low fractality

Fractional conformable attractors with low fractality

Mathematical modeling approach to the fractional Bergman's model

Application of the Caputo‐Fabrizio and Atangana‐Baleanu fractional derivatives to mathematical model of cancer chemotherapy effect

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