Browsing by Author "Ahmed, I."

Now showing 1 - 3 of 3

Citation - Scopus: 25
A Caputo-Fabrizio Fractional-Order Cholera Model and Its Sensitivity Analysis
(Mehmet Yavuz, 2023) Akgül, A.; Jarad, F.; Kumam, P.; Nonlaopon, K.; Ahmed, I.; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In recent years, the availability of advanced computational techniques has led to a growing emphasis on fractional-order derivatives. This development has enabled researchers to explore the intricate dynamics of various biological models by employing fractional-order derivatives instead of traditional integer-order derivatives. This paper proposes a Caputo-Fabrizio fractional-order cholera epidemic model. Fixed-point theorems are utilized to investigate the existence and uniqueness of solutions. A recent and effective numerical scheme is employed to demonstrate the model’s complex behaviors and highlight the advantages of fractional-order derivatives. Additionally, a sensitivity analysis is conducted to identify the most influential parameters. © 2023 by the authors.
Citation - Scopus: 9
A Dynamical and Sensitivity Analysis of the Caputo Fractional-Order Ebola Virus Model: Implications for Control Measures
(Thammasat University, 2023) Ahmed, I.; Jarad, Fahd; Yusuf, A.; Tariboon, J.; Muhammad, M.; Jarad, F.; Mikailu, B.B.; 234808; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The recurrence of outbreaks in cases of Ebola virus among African countries remains one of the greatest issues of concern. Practices such as hunting or consumption of contam-inated bush meat, unsafe funeral practices, and environmental contamination have all been implicated as possible contributors. This paper investigates the transmission dynamics of the Ebola virus model in the setting of a Caputo fractional-order derivative that accounts for both direct and indirect transmissions of the virus. By employing the concept of fixed theorems, we derived the existence and uniqueness results of the model. Moreover, we analyzed the forward normalized sensitivity indices to identify the critical parameters for controlling the infection and found that reducing the contact rate between infected individuals and susceptible vectors is vital to limiting the virus’s spread. Comparing the proposed fractional-order model with those of the previously developed integer-order model numerically, we found that the proposed model provides more reliable information on the model’s dynamics. Thus, we conclude that the Caputo fractional-order operator is a precise tool for describing the proposed model behavior and can help understand the complexities of Ebola virus disease outbreaks. © 2023, Thammasat University. All rights reserved.
Citation - Scopus: 3
Numerical Construction of Lyapunov Functions Using Homotopy Continuation Method
(DergiPark, 2022) Bala, S.I.; Ahmed, I.; Ibrahim, M.J.; Jarad, F.; Ibrahim, A.; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Lyapunov functions are commonly involved in the analysis of the stability of linear and nonlinear dynamical systems. Despite the fact that there is no generic procedure for creating these functions, many authors use polynomials in p-forms as candidates for constructing Lyapunov functions, while others restrict the construction to quadratic forms. We proposed a method for constructing polynomial Lyapunov functions that are not necessary in a form by focusing on the positive and negative definiteness of the Lyapunov candidate and the Hessian of its derivative, as well as employing the sum of square decomposition. The idea of Newton polytopes was used to transform the problem into a system of algebraic equations that were solved using the polynomial homotopy continuation method. Our method can produce several possibilities of Lyapunov functions for a given candidate. The sample test conducted demonstrates that the method developed is promising. © 2022, DergiPark. All rights reserved.