Analytical solutions of the Keller-Segel chemotaxis model involving fractional operators without singular kernel

Morales‐Delgado, V. F.; Gómez-Aguilar, J. F.; Kumar, Sunil; Taneco-Hernández, M.A.

doi:10.1140/epjp/i2018-12038-6

Cited by 33 publications

(15 citation statements)

References 28 publications

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“…The convergence analysis of the series solution is presented in [24]. Applying the aforesaid technique, in this work, two fractional mathematical models are considered.…”

mentioning

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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“…The convergence analysis of the series solution is presented in [24]. Applying the aforesaid technique, in this work, two fractional mathematical models are considered.…”

mentioning

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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“…where the unidentified function μ(ζ, Ψ) defines the concentrations of amoebae, the chemical concentration is denoted by ρ(ζ, Ψ), and the chemotactic is defined by the partial derivative of z/zζ μ(ζ, Ψ)z[χρ(ζ, ψ)]/zζ , χ(ρ) is the sensitivity function. Some other types of sensitivity functions can be observed in the coupled time-fractional K-S chemotactic model in [40] and also in the K-S model with a logic sensitivity function and small diffusivity [41]. Also, singular sensitivity can be seen in the system of the two-dimensional K-S system in [36,42,43].…”

Section: Introductionmentioning

confidence: 92%

On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions

et al. 2020

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In this paper, the fractional view analysis of the Keller–Segal equations with sensitivity functions is presented. The Caputo operator has been used to pursue the present research work. The natural transform is combined with the homotopy perturbation method, and a new scheme for implementation is derived. The modified established method is named as the homotopy perturbation transform technique. The derived results are compared with the solution of the Laplace Adomian decomposition technique by using the systems of fractional Keller–Segal equations. The solution graphs and the table have shown that the obtained results coincide with the solution of the Laplace Adomian decomposition method. Fractional-order solutions are determined to confirm the reliability of the current method. It is observed that the solutions at various fractional orders are convergent to an integer-order solution of the problems. The suggested procedure is very attractive and straight forward and therefore can be modified to solve high nonlinear fractional partial differential equations and their systems.

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“…Definition 3 (see [42]). e fractional generalized Mittag-Leffler law with the sense of Atangana-Baleanu operator is defined as follows:…”

Section: Fractional Calculusmentioning

confidence: 99%

“…e Laplace homotopy perturbation transform technique is a mixture of the homotopy perturbation technique introduced by Liao [41] and of the Laplace transformation [42]. e rest of the paper is arranged as follows.…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators

et al. 2021

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This paper aims to implement an analytical method, known as the Laplace homotopy perturbation transform technique, for the result of fractional-order Whitham–Broer–Kaup equations. The technique is a mixture of the Laplace transformation and homotopy perturbation technique. Fractional derivatives with Mittag-Leffler and exponential laws in sense of Caputo are considered. Moreover, this paper aims to show the Whitham–Broer–Kaup equations with both derivatives to see their difference in a real-world problem. The efficiency of both operators is confirmed by the outcome of the actual results of the Whitham–Broer–Kaup equations. Some problems have been presented to compare the solutions achieved with both fractional-order derivatives.

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Analytical solutions of the Keller-Segel chemotaxis model involving fractional operators without singular kernel

Cited by 33 publications

References 28 publications

Mathematical modeling approach to the fractional Bergman's model

Mathematical modeling approach to the fractional Bergman's model

On the Fractional View Analysis of Keller–Segel Equations with Sensitivity Functions

Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators

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