Mathematical modelling of growth of tumour cells with chemotherapeutic cells by using Yang–Abdel–Cattani fractional derivative operator

Mishra, Manvendra Narayan; Aljohani, Abdulrahman F.

doi:10.1080/16583655.2022.2146572

Cited by 18 publications

(2 citation statements)

References 40 publications

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“…The time fractional analysis by the Yang–Abdel–Cattani has many industrial applications for example in the field of medial it is used to design a mathematical model for the growth of the tumor cells with chemotherapeutic cells 36 . The time fractional approach is used to analyze of stuxnet virus fractional growth in the industrial control system 37 .…”

Section: Introductionmentioning

confidence: 99%

Time fractional Yang–Abdel–Cattani derivative in generalized MHD Casson fluid flow with heat source and chemical reaction

Sehra,

Sadia,

Haq

et al. 2023

Sci Rep

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This present research article investigates the exact analytical solution for the mathematical model of the generalized Casson fluid flow by using the new fractional operator with Rabotnov exponential kernel i.e. Yang–Abdel–Cattani operator. The impacts of heat source, magnetic hydrodynamics and chemical reactions on the flow of fractional Casson fluid through a vertical flat plate are studied in this article. For the sake of a better interpretation of the rheological behavior of Casson fluid we have used the new operator of fractional order with exponential kernel of Rabotnov known as Yang–Abdel–Cattani operator of fractional derivative. By making use of the technique of Laplace transform we have find the exact analytical solution of the problem in the Mittag–Leffler’s form, for all the three governing equations i.e. Velocity, energy and concentration equation. It has been noticed from the literature that it is challenging to obtain analytical results from fractional fluid model derived by the various fractional operators. This article helps to address this issue by providing analytical solutions for fractionalized fluid models. To analyze the physical importance of different fluid parameters such as Schmidt number, Prandtl number, MHD and alpha on the heat, mass and momentum class are presented through graphs. The concentration of the fluid decreases with Schmidth number and temperature of the fluid decreases with the increasing Prandtl number. The velocity of the fluid decreases with increasing MHD effects and increases with increasing Alpha. The Yang–Abdel–Cattani operator of fractional order can describe the memory effects more suitably than the other fractional operators.

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Section: Introductionmentioning

confidence: 99%

Time fractional Yang–Abdel–Cattani derivative in generalized MHD Casson fluid flow with heat source and chemical reaction

Sehra,

Sadia,

Haq

et al. 2023

Sci Rep

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“…Fractional calculus also overcomes the issue that the theory of the classical integer-order differential model does not agree well with the experimental results, and fractional calculus only needs to use a few parameters to obtain better results [7,8].Fractional-order differential operators are effectively applied to numerical analysis tools in physics, mechanics, science, and mathematics. Compared to integer calculus, fractional calculus provides us with better discoveries than traditional models [9]. Ref.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and Stability Analysis of a New Fractional-Order Prey–Predator Model with Fear Effects in Toxic Injections

Liu,

Chen,

et al. 2023

Mathematics

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This paper proposes a prey–predator model affected by fear effects and toxic substances. We used the Lipschitz condition to prove the uniqueness of the model solution and Laplace transform to prove the boundedness of the model solution. We used the fractional-order stability theorem to provide sufficient conditions for the local stability of equilibrium points, and selected fractional-order derivatives as parameters to perform Hopf bifurcation analysis on the system. Finally, the theoretical results are verified via numerical simulation. The results show that a value of α will affect the stability of the system and that the population size and the effect of toxic substances have a huge impact on the stability of the system.

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Mathematical modelling of diphtheria transmission and vaccine efficacy using Nigeria

Olayiwola,

Alaje

2024

Model. Earth Syst. Environ.

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Mathematical modelling of growth of tumour cells with chemotherapeutic cells by using Yang–Abdel–Cattani fractional derivative operator

Cited by 18 publications

References 40 publications

Time fractional Yang–Abdel–Cattani derivative in generalized MHD Casson fluid flow with heat source and chemical reaction

Time fractional Yang–Abdel–Cattani derivative in generalized MHD Casson fluid flow with heat source and chemical reaction

Bifurcation and Stability Analysis of a New Fractional-Order Prey–Predator Model with Fear Effects in Toxic Injections

Mathematical modelling of diphtheria transmission and vaccine efficacy using Nigeria

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