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    Öğe
    A SARS-CoV-2 Fractional-Order Mathematical Model via the Modified Euler Method
    (Mdpi, 2022) Ul Haq, Ihtisham; Yavuz, Mehmet; Ali, Nigar; Akgul, Ali
    This article develops a within-host viral kinetics model of SARS-CoV-2 under the Caputo fractional-order operator. We prove the results of the solution's existence and uniqueness by using the Banach mapping contraction principle. Using the next-generation matrix method, we obtain the basic reproduction number. We analyze the model's endemic and disease-free equilibrium points for local and global stability. Furthermore, we find approximate solutions for the non-linear fractional model using the Modified Euler Method (MEM). To support analytical findings, numerical simulations are carried out.
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    Öğe
    Analysis of fractal fractional Lorenz type and financial chaotic systems with exponential decay kernels
    (Amer Inst Mathematical Sciences-Aims, 2022) Ul Haq, Ihtisham; Ahmad, Shabir; Saifullah, Sayed; Nonlaopon, Kamsing; Akgul, Ali
    In this work, we formulate a fractal fractional chaotic system with cubic and quadratic nonlinearities. A fractal fractional chaotic Lorenz type and financial systems are studied using the Caputo Fabrizo (CF) fractal fractional derivative. This study focuses on the characterization of the chaotic nature, and the effects of the fractal fractional-order derivative in the CF sense on the evolution and behavior of each proposed systems. The stability of the equilibrium points for the both systems are investigated using the Routh-Hurwitz criterion. The numerical scheme, which includes the discretization of the CF fractal-fractional derivative, is used to depict the phase portraits of the fractal fractional chaotic Lorenz system and the fractal fractional-order financial system. The simulation results presented in both cases include the two- and three-dimensional phase portraits to evaluate the applications of the proposed operators.
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    Öğe
    Mathematical modelling of COVID-19 outbreak using caputo fractional derivative: stability analysis
    (Taylor & Francis Ltd, 2024) Ul Haq, Ihtisham; Ali, Nigar; Bariq, Abdul; Akgul, Ali; Baleanu, Dumitru; Bayram, Mustafa
    The novel coronavirus SARS-Cov-2 is a pandemic condition and poses a massive menace to health. The governments of different countries and their various prohibitory steps to restrict the virus's expanse have changed individuals' communication processes. Due to physical and financial factors, the population's density is more likely to interact and spread the virus. We establish a mathematical model to present the spread of the COVID-19 in worldwide. In this article, we propose a novel mathematical model (' $ \mathbb {S}\mathbb {L}\mathbb {I}\mathbb {I}_{q}\mathbb {I}_{h}\mathbb {R}\mathbb {P} $ SLIIqIhRP') to assess the impact of using hospitalization, quarantine measures, and pathogen quantity in controlling the COVID-19 pandemic. We analyse the boundedness of the model's solution by employing the Laplace transform approach to solve the fractional Gronwall's inequality. To ensure the uniqueness and existence of the solution, we rely on the Picard-Lindelof theorem. The model's basic reproduction number, a crucial indicator of epidemic potential, is determined based on the greatest eigenvalue of the next-generation matrix. We then employ stability theory of fractional differential equations to qualitatively examine the model. Our findings reveal that both locally and globally, the endemic equilibrium and disease-free solutions demonstrate symptomatic stability. These results shed light on the effectiveness of the proposed interventions in managing and containing the COVID-19 outbreak.