Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 47Citation - Scopus: 48Oscillatory and Complex Behaviour of Caputo-Fabrizio Fractional Order Hiv-1 Infection Model(Amer inst Mathematical Sciences-aims, 2022) Ullah, Aman; Partohaghighi, Mohammad; Saifullah, Sayed; Akgul, Ali; Jarad, Fahd; Ahmad, ShabirHIV-1 infection is a dangerous diseases like Cancer, AIDS, etc. Many mathematical models have been introduced in the literature, which are investigated with different approaches. In this article, we generalize the HIV-1 model through nonsingular fractional operator. The non-integer mathematical model of HIV-1 infection under the Caputo-Fabrizio derivative is presented in this paper. The concept of Picard-Lindelof and fixed-point theory are used to address the existence of a unique solution to the HIV-1 model under the suggested operator. Also, the stability of the suggested model is proved through the Picard iteration and fixed point theory approach. The model's approximate solution is constructed through three steps Adams-Bashforth numerical method. Numerical simulations are provided for different values of fractional-order to study the complex dynamics of the model. Lastly, we provide the oscillatory and chaotic behavior of the proposed model for various fractional orders.Article Citation - WoS: 20Citation - Scopus: 21Fractional Order Mathematical Model of Serial Killing With Different Choices of Control Strategy(Mdpi, 2022) Ahmad, Shabir; Arfan, Muhammad; Akgul, Ali; Jarad, Fahd; Rahman, Mati UrThe current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag-Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem and establish a result that ensures the existence of at least one solution. Ulam's stability of the given model is presented by using nonlinear concepts. The iterative fractional-order Adams-Bashforth approach is being used to find the approximate solution. The suggested method is numerically simulated at various fractional orders. The simulation is carried out for various control strategies. Over time, all of the compartments demonstrate convergence and stability. Different fractional orders have produced an excellent comparison outcome, with low fractional orders achieving stability sooner.Article Citation - WoS: 36Citation - Scopus: 39Analysis of Fractional Order Chaotic Financial Model With Minimum Interest Rate Impact(Mdpi, 2020) Akgul, Ali; Baleanu, Dumitru; Imtiaz, Sumaiyah; Ahmad, Aqeel; Farman, MuhammadThe main objective of this paper is to construct and test fractional order derivatives for the management and simulation of a fractional order disorderly finance system. In the developed system, we add the critical minimum interest ratedparameter in order to develop a new stable financial model. The new emerging paradigm increases the demand for innovation, which is the gateway to the knowledge economy. The derivatives are characterized in the Caputo fractional order derivative and Atangana-Baleanu derivative. We prove the existence and uniqueness of the solutions with fixed point theorem and an iterative scheme. The interest rate begins to rise according to initial conditions as investment demand and price exponent begin to fall, which shows the financial system's actual macroeconomic behavior. Specifically component of its application to the large scale and smaller scale forms, just as the utilization of specific strategies and instruments such fractal stochastic procedures and expectation.