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

Morales‐Delgado, V. F.; Gómez-Aguilar, J. F.; Saad, Khaled M.; Escobar-Jiménez, R.F.

doi:10.1002/mma.5421

Cited by 50 publications

(21 citation statements)

References 57 publications

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“…Atangana-Baleanu operator has a non-singular and non-local (that is, Mittag-Leffler) kernel while the Caputo operator does not [41,42]. From the biological meanings, a model with Atangana-Baleanu operator gives better results in applying memory effects [43][44][45]. Nevertheless, the Caputo operator has more complex analytical tools in investigating the dynamics of the model such as the local stability [46][47][48][49][50], the global stability [51,52], bifurcation theory [52][53][54], and so on.…”

Section: Variables and Parameters Description X(t)mentioning

confidence: 99%

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

Panigoro

Suryanto

Kusumawinahyu

et al. 2020

Axioms

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The harvesting management is developed to protect the biological resources from over-exploitation such as harvesting and trapping. In this article, we consider a predator–prey interaction that follows the fractional-order Rosenzweig–MacArthur model where the predator is harvested obeying a threshold harvesting policy (THP). The THP is applied to maintain the existence of the population in the prey–predator mechanism. We first consider the Rosenzweig–MacArthur model using the Caputo fractional-order derivative (that is, the operator with the power-law kernel) and perform some dynamical analysis such as the existence and uniqueness, non-negativity, boundedness, local stability, global stability, and the existence of Hopf bifurcation. We then reconsider the same model involving the Atangana–Baleanu fractional derivative with the Mittag–Leffler kernel in the Caputo sense (ABC). The existence and uniqueness of the solution of the model with ABC operator are established. We also explore the dynamics of the model with both fractional derivative operators numerically and confirm the theoretical findings. In particular, it is shown that models with both Caputo operator and ABC operator undergo a Hopf bifurcation that can be controlled by the conversion rate of consumed prey into the predator birth rate or by the order of fractional derivative. However, the bifurcation point of the model with the Caputo operator is different from that of the model with the ABC operator.

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Section: Variables and Parameters Description X(t)mentioning

confidence: 99%

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

Panigoro

Suryanto

Kusumawinahyu

et al. 2020

Axioms

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“…Ghanbari and Atangana [14] used the Atangana-Baleanu definition for the fractional derivative to introduce the new fractional mask for image denoising. Morales-Delgado et al [15] obtained solutions of a cancer chemotherapy effect model involving the Caputo-Fabrizio and Atanagana-Baleanu fractional derivatives. There are some papers considering the fractional-order derivate implemented in the compartment models.…”

Section: Introductionmentioning

confidence: 99%

Fractional-Order SIR Epidemic Model for Transmission Prediction of COVID-19 Disease

2020

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In this paper, the fractional-order generalization of the susceptible-infected-recovered (SIR) epidemic model for predicting the spread of the COVID-19 disease is presented. The time-domain model implementation is based on the fixed-step method using the nabla fractional-order difference defined by Grünwald-Letnikov formula. We study the influence of fractional order values on the dynamic properties of the proposed fractional-order SIR model. In modeling the COVID-19 transmission, the model’s parameters are estimated while using the genetic algorithm. The model prediction results for the spread of COVID-19 in Italy and Spain confirm the usefulness of the introduced methodology.

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“…The ABFD contains the Mittag-Leffler function that is the cornerstone of the fractional calculus. Applications of the Atangana-Baleanu operator have been explored in fields as diverse as heat transfer [9], chaos theory [10], oscillators [11], the hepatitis E virus model [12], cancer chemotherapy [13], smoking model [14] and coronavirus [15].…”

Section: Introductionmentioning

confidence: 99%

An efficient technique based on cubic B-spline functions for solving time-fractional advection diffusion equation involving Atangana–Baleanu derivative

Shafiq

Abbas

Abualnaja

et al. 2021

Engineering with Computers

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The present paper deals with cubic B-spline approximation together with -weighted scheme to obtain numerical solution of the time fractional advection diffusion equation using Atangana-Baleanu derivative. To discretize the Atangana-Baleanu time derivative containing a non-singular kernel, finite difference scheme is utilized. The cubic basis functions are associated with spatial discretization. The current discretization scheme used in the present study is unconditionally stable and the convergence is of order O(h 2 + Δt 2 ) . The proposed scheme is validated through some numerical examples which reveal the current scheme is feasible and quite accurate.

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

Cited by 50 publications

References 57 publications

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

A Rosenzweig–MacArthur Model with Continuous Threshold Harvesting in Predator Involving Fractional Derivatives with Power Law and Mittag–Leffler Kernel

Fractional-Order SIR Epidemic Model for Transmission Prediction of COVID-19 Disease

An efficient technique based on cubic B-spline functions for solving time-fractional advection diffusion equation involving Atangana–Baleanu derivative

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