Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Now showing 1 - 8 of 8
  • Article
    Citation - WoS: 38
    Citation - Scopus: 39
    On the Mittag-Leffler Stability of Q-Fractional Nonlinear Dynamical Systems
    (Editura Acad Romane, 2011) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Abdeljawad, Thabet; Gundogdu, Emrah; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
    In this article, analogous to the definition of the exponential stability of ordinary dynamical systems and the Mittag-Leffler stability of the fractional dynamical systems, we consider the Mittag-Leffler stability for q-fractional nonlinear dynamical systems. The sufficient conditions for Mittag-Leffler stability of such dynamical systems within the framework of the q-fractional Caputo derivative are studied.
  • Article
    Citation - WoS: 1
    Citation - Scopus: 3
    Hopf Bifurcations of a Lengyel-Epstein Model Involving Two Discrete Time Delays
    (Amer inst Mathematical Sciences-aims, 2022) Bilazeroglu, Seyma; Merdan, Huseyin; Guerrini, Luca
    Hopf bifurcations of a Lengyel-Epstein model involving two discrete time delays are investigated. First, stability analysis of the model is given, and then the conditions on parameters at which the system has a Hopf bifurcation are determined. Second, bifurcation analysis is given by taking one of delay parameters as a bifurcation parameter while fixing the other in its stability interval to show the existence of Hopf bifurcations. The normal form theory and the center manifold reduction for functional differential equations have been utilized to determine some properties of the Hopf bifurcation including the direction and stability of bifurcating periodic solution. Finally, numerical simulations are performed to support theoretical results. Analytical results together with numerics present that time delay has a crucial role on the dynamical behavior of Chlorine Dioxide-Iodine-Malonic Acid (CIMA) reaction governed by a system of nonlinear differential equations. Delay causes oscillations in the reaction system. These results are compatible with those observed experimentally.
  • Article
    Citation - Scopus: 1
    Numerical Investigation of Malaria Disease Dynamics in Fuzzy Environment
    (Tech Science Press, 2023) Baleanu, Dumitru; Ahmed, Nauman; Awrejcewicz, Jan; Rafiq, Muhammad; Raza, Ali; Ahmad, Muhammad Ozair; Dayan, Fazal
    The application of fuzzy theory is vital in all scientific disciplines. The construction of mathematical models with fuzziness is little studied in the literature. With this in mind and for a better understanding of the disease, an SEIR model of malaria transmission with fuzziness is examined in this study by extending a classical model of malaria transmission. The parameters beta and delta, being function of the malaria virus load, are considered fuzzy numbers. Three steady states and the reproduction number of the model are analyzed in fuzzy senses. A numerical technique is developed in a fuzzy environment to solve the studied model, which retains essential properties such as positivity and dynamic consistency. Moreover, numerical simulations are carried out to illustrate the analytical results of the developed technique. Unlike most of the classical methods in the literature, the proposed approach converges unconditionally and can be considered a reliable tool for studying malaria disease dynamics.
  • Article
    Citation - WoS: 6
    Citation - Scopus: 11
    Modeling of Computer Virus Propagation With Fuzzy Parameters
    (Tech Science Press, 2023) Ahmed, Nauman; Baleanu, Dumitru; Fatima, Umbreen; Dayan, Fazal; Rafiq, Muhammad; Mahmoud, Emad E.; Alhebshi, Reemah M.
    Typically, a computer has infectivity as soon as it is infected. It is a reality that no antivirus programming can identify and eliminate all kinds of viruses, suggesting that infections would persevere on the Internet. To understand the dynamics of the virus propagation in a better way, a computer virus spread model with fuzzy parameters is presented in this work. It is assumed that all infected computers do not have the same contribution to the virus transmission process and each computer has a different degree of infectivity, which depends on the quantity of virus. Considering this, the parameters beta and gamma being functions of the computer virus load, are considered fuzzy numbers. Using fuzzy theory helps us understand the spread of computer viruses more realistically as these parameters have fixed values in classical models. The essential features of the model, like reproduction number and equilibrium analysis, are discussed in fuzzy senses. Moreover, with fuzziness, two numerical methods, the forward Euler technique, and a nonstandard finite difference (NSFD) scheme, respectively, are developed and analyzed. In the evidence of the numerical simulations, the proposed NSFD method preserves the main features of the dynamic system. It can be considered a reliable tool to predict such types of solutions.
  • Article
    Hyers-Ulam Stability of Fractional Stochastic Differential Equations With Random Impulse
    (Korean Mathematical Soc, 2023) Baleanu, Dumitru; Kandasamy, Banupriya; Kasinathan, Ramkumar; Kasinathan, Ravikumar; Sandrasekaran, Varshini
    The goal of this study is to derive a class of random impulsive non-local fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Computational Analysis for Computer Network Model With Fuzziness
    (Tech Science Press, 2023) Baleanu, Dumitru; Dayan, Fazal; Ullah, Sami; Ahmed, Nauman; Rafiq, Muhammad; Raza, Ali; Alfwzan, Wafa F.
    A susceptible, exposed, infectious, quarantined and recovered (SEIQR) model with fuzzy parameters is studied in this work. Fuzziness in the model arises due to the different degrees of susceptibility, exposure, infectivity, quarantine and recovery among the computers under consideration due to the different sizes, models, spare parts, the surrounding environments of these PCs and many other factors like the resistance capacity of the individual PC against the virus, etc. Each individual PC has a different degree of infectivity and resistance against infection. In this scenario, the fuzzy model has richer dynamics than its classical counterpart in epidemiology. The reproduction number of the developed model is studied and the equilibrium analysis is performed. Two different techniques are employed to solve the model numerically. Numerical simulations are performed and the obtained results are compared. Positivity and convergence are maintained by the suggested technique which are the main features of the epidemic models.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 15
    Numerical Investigation of Space Fractional Order Diffusion Equation by the Chebyshev Collocation Method of the Fourth Kind and Compact Finite Difference Scheme
    (Amer inst Mathematical Sciences-aims, 2021) Safdari, Hamid; Azari, Yaqub; Jafari, Hossein; Baleanu, Dumitru; Aghdam, Yones Esmaeelzade
    This paper develops a numerical scheme for finding the approximate solution of space fractional order of the diffusion equation (SFODE). Firstly, the compact finite difference (CFD) with convergence order O(delta tau 2) is used for discretizing time derivative. Afterwards, the spatial fractional derivative is approximated by the Chebyshev collocation method of the fourth kind. Furthermore, time-discrete stability and convergence analysis are presented. Finally, two examples are numerically investigated by the proposed method. The examples illustrate the performance and accuracy of our method compared to existing methods presented in the literature. 1. Introduction. One of the issues which have garnered researchers' attention these days is the fractional differential equations (FDEs) and have been numerically investigated by a huge number of authors [2, 3, 8, 9, 16, 21, 23, 25, 28, 29]. Fractional calculus is involved in many applications of science and engineering such as economics, physics, optimal control, and other applications, see [10, 11, 13, 19, 22, 26, 33, 34, 35]. A case in point is the diffusion and reaction-diffusion models in
  • Article
    Citation - WoS: 11
    Citation - Scopus: 13
    On Solving Fractional Mobile/Immobile Equation
    (Sage Publications Ltd, 2017) Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Pourbashash, Hossein
    In this article, a numerical efficient method for fractional mobile/immobile equation is developed. The presented numerical technique is based on the compact finite difference method. The spatial and temporal derivatives are approximated based on two difference schemes of orders O(T2-alpha) and O(h(4)), respectively. The proposed method is unconditionally stable and the convergence is analyzed within Fourier analysis. Furthermore, the solvability of the compact finite difference approach is proved. The obtained results show the ability of the compact finite difference.