Existence, Uniqueness and Approximate Controllability of Impulsive Fractional Nonlinear Control System with Nonsingular Kernel

Naji, Fadhil Abbas; Al-Shara'a, Iftichar Mudhar Talb

doi:10.24996/ijs.2022.63.9.25

Cited by 1 publication

(1 citation statement)

References 13 publications

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“…( 2022 ); Danane et al. ( 2021 ), control theory Naji and Al-Sharaa ( 2022 ), biology Hattaf and Yousfi ( 2020 ); Magin ( 2009 ) and engineering Debnath ( 2003 ). The main advantage of using fractional operators is that they can correctly describe the dynamics of real problems at any time.…”

Section: Introductionmentioning

confidence: 99%

Modelling disease spread with spatio-temporal fractional derivative equations and saturated incidence rate

Bounkaicha

Allali

2023

Model. Earth Syst. Environ.

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The global analysis of a spatio-temporal fractional order SIR infection model with saturated incidence function is suggested and studied in this paper. The dynamics of the infection is described by three partial differential equations including a time-fractional derivative order for each one of them. The equations of our model describe the evolution of the susceptible, the infected and the recovered individuals with taking into account the spatial diffusion for each compartment. We will choose a saturated incidence rate in order to describe the nonlinear force of the infection. First, we will prove the well-posedness of our suggested model in terms of existence and uniqueness of the solution. Also in this context, the boundedness and the positivity of solutions are established. Afterward, we will give the forms of the disease-free equilibrium and the endemic one. It was demonstrated that the global stability of the each equilibrium depends mainly on the basic reproduction number. Finally, numerical simulations are performed to validate the theoretical results and to show the effect of vaccination in reducing the infection severity. It was shown that the fractional derivative order has no effect on the equilibria stability but only on the convergence speed towards the steady states. It was also observed that vaccination is amongst the good strategies in controlling the disease spread.

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