Mathematical structure of mosaic disease using microbial biostimulants via Caputo and Atangana–Baleanu derivatives

Kumar, Pushpendra; Ertürk, Vedat Suat; Almusawa, Hassan

doi:10.1016/j.rinp.2021.104186

Cited by 43 publications

(13 citation statements)

References 32 publications

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“…For example, fractional models have been proposed to study the effects of malaria infection on mosquito biting behavior, and the attractiveness of humans are considered (Abboubakar et al , 2020). A proposed study on the role of natural microbial biostimulants to increase plant performance and protecting them against mosaic infection has been conducted using fractional nonlinear models (Kumar et al , 2021a). More recent research on fractional models arise in health sciences can be viewed in (Kumar et al , 2021b; Manickam et al , 2022; Kumar et al , 2022).…”

Section: Introductionmentioning

confidence: 99%

Solution of a nonlinear fractional COVID-19 model

Abukhaled

Khuri

Rabah

2022

HFF

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Purpose The purpose of this study is to obtain an analytical solution for a nonlinear system of the COVID-19 model for susceptible, exposed, infected, isolated and recovered. Design/methodology/approach The Laplace decomposition method and the differential transformation method are used. Findings The obtained analytical results are useful on two fronts: first, they would contribute to a better understanding of the dynamic spread of the COVID-19 disease and help prepare effective measures for prevention and control. Second, researchers would benefit from these results in modifying the model to study the effect of other parameters such as partial closure, awareness and vaccination of isolated groups on controlling the pandemic. Originality/value The approach presented is novel in its implementation of the nonlinear system of the COVID-19 model

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Section: Introductionmentioning

confidence: 99%

Solution of a nonlinear fractional COVID-19 model

Abukhaled

Khuri

Rabah

2022

HFF

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“…[ 33 ]. Study given in [ 34 ] discusses the mathematical structure of mosaic epidemic. A new, efficient and easy algorithm to solve the generalised Caputo-type fractional-order initial value problems is given in ref.…”

Section: Introductionmentioning

confidence: 99%

A study on the dynamics of alkali–silica chemical reaction by using Caputo fractional derivative

Kumar¹,

Govindaraj²,

Ertürk

et al. 2022

Pramana - J Phys

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In this paper, we propose a mathematical study to simulate the dynamics of alkali–silica reaction (ASR) by using the Caputo fractional derivative. We solve a non-linear fractional-order system containing six differential equations to understand the ASR. For proving the existence of a unique solution, we use some recent novel properties of Mittag–Leffler function along with the fixed point theory. The stability of the proposed system is also proved by using Ulam–Hyers technique. For deriving the fractional-order numerical solution, we use the well-known Adams–Bashforth–Moulton scheme along with its stability. Graphs are plotted to understand the given chemical reaction practically. The main reason to use the Caputo-type fractional model for solving the ASR system is to propose a novel mathematical formulation through which the ASR mechanism can be efficiently explored. This paper clearly shows the importance of fractional derivatives in the study of chemical reactions.

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“…Hopf bifurcations can happen in delayed models and have been studied in [20] for an SIRS (susceptible, infective, recovered, susceptible) model and in [17,21] for a plant-virus model. Fractional derivatives have also been introduced in [22,23]. Models have also been introduced for the within-plant interactions with the virus.…”

Section: Introductionmentioning

confidence: 99%

Delays in Plant Virus Models and Their Stability

Chen-Charpentier

2022

Mathematics

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Viruses infect humans and animals but also infect plants and cause great economic and ecological damage. In most cases, the virus is transmitted by a vector. After being bitten by an infected vector, the virus takes some time to replicate and spread in the plant. We present two models of the spread of viruses in plants based on ordinary differential equations, and then add either a delay or an exposed plant population. We study two ways of adding the delay. In the first one, a plant infected by a vector changes from susceptible to infective after a time equal to the delay. In the second one, immediately after the contact between a susceptible plant and infective vector, the plant is no longer susceptible, but it takes time equal to the delay for it to turn infective. To better explain the two ways of incorporating the delays, we first introduce them in a simple SIRS model. We analyze the models and study their stability numerically. We conclude by studying the interactions and the conservation of the total plant population that the first way of introducing the delay is better justified.

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Mathematical structure of mosaic disease using microbial biostimulants via Caputo and Atangana–Baleanu derivatives

Cited by 43 publications

References 32 publications

Solution of a nonlinear fractional COVID-19 model

Solution of a nonlinear fractional COVID-19 model

A study on the dynamics of alkali–silica chemical reaction by using Caputo fractional derivative

Delays in Plant Virus Models and Their Stability

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