Analysis of fractional‐order nonlinear dynamic systems under Caputo differential operator

Yusuf, Abdullahi; Acay, Bahar

doi:10.1002/mma.7454

Cited by 3 publications

(1 citation statement)

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“…Finally, numerical simulations were presented to illustrate their obtained theoretical results. On the other hand, because the memory effect plays a vital role in the application, Yusuf et al 38 utilized an advantageous nonlocal fractional operator to investigate and analyze a mathematical model of the planktonic ecosystem and biological system for the ecosystem on Planet GLIA‐2. They discussed the existence and uniqueness of the solutions for both models with the help of the fixed‐point theorem, which were obtained by the first‐order convergent numerical technique that is accurate, conditionally stable, and convergent.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics and bifurcation analysis of a fractional‐order SEIR epidemic model with saturation incidence rate

Ghori

Naik

et al. 2022

Math Methods in App Sciences

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The present paper studies a fractional‐order SEIR epidemic model for the transmission dynamics of infectious diseases such as HIV and HBV that spreads in the host population. The total host population is considered bounded, and Holling type‐II saturation incidence rate is involved as the infection term. Using the proposed SEIR epidemic model, the threshold quantity, namely, basic reproduction number scriptR0, is obtained that determines the status of the disease, whether it dies out or persists in the whole population. The model's analysis shows that two equilibria exist, namely, disease‐free equilibrium (DFE) and endemic equilibrium (EE). The global stability of the equilibria is determined using a Lyapunov functional approach. The disease status can be verified based on obtained threshold quantity scriptR0. If scriptR0<1, then DFE is globally stable, leading to eradicating the population's disease. If scriptR0>1, a unique EE exists, and that is globally stable under certain conditions in the feasible region. The Caputo type fractional derivative is taken as the fractional operator. The bifurcation and sensitivity analyses are also performed for the proposed model that determines the relative importance of the parameters in disease transmission. The numerical solution of the model is obtained by the generalized Adams–Bashforth–Moulton method. Finally, numerical simulations are performed to illustrate and verify the analytical results. From the obtained results, it is concluded that the order of the fractional derivative plays a significant role in the dynamic process. Also, from the sensitivity analysis results, it is seen that the parameter δ ( infection rate) is positively correlated to scriptR0, while the parameter μ (inhibition rate) is negatively correlated to scriptR0, which means these parameters are more sensitive than others in disease dynamics.

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Section: Introductionmentioning

confidence: 99%