Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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  • Article
    Citation - WoS: 7
    On Dynamics of Fractional-Order Model of Hcv Infection
    (Univ Prishtines, 2017) Khodabakhshi, Neda; Baleanu, Dumitru; Vaezpour, S. Mansour; Baleanu, Dumitru; Matematik
    In this paper, we investigate the dynamical behavior of the fractional-order model within Caputo derivative of HCV infection. Stability analysis of the equilibrium points is according to the basic reproduction number R-0. The numerical simulations are also presented to illustrate the results.
  • Article
    Citation - WoS: 60
    Citation - Scopus: 68
    Lyapunov-Krasovskii Stability Theorem for Fractional Systems With Delay
    (Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, D.; Ranjbar N, A.; Abdeljawad, Thabet; Sadati R, S. J.; Delavari, R. H.; Abdeljawad (Maraaba), T.; Gejji, V.; Matematik
    Fractional calculus techniques and methods started to be applied during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative and we extended Lyapunov-Krasovskii theorem for the fractional nonlinear systems.
  • 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
    Effects of the Random Walk and the Maturation Period in a Diffusive Predator-Prey System With Two Discrete Delays
    (Pergamon-elsevier Science Ltd, 2023) Goktepe, S.; Merdan, H.; Bilazeroglu, S.
    This study aims to present a complete Hopf bifurcation analysis of a model describing the relationship between prey and predator. A ratio-dependent reaction-diffusion system with two discrete time delays operating under Neumann boundary conditions governs the model that represents this competition. The bifurcation parameter for the analysis is a delay parameter that reflects the amount of time needed for the predator to be able to hunt. Bilazeroglu and Merdan's algorithm (Bilazeroglu et al., 2021), which is developed by using the center manifold theorem and normal form theory, is used to establish the existence of Hopf bifurcations and also the stability of the bifurcating periodic solutions. The same procedure is used to illustrate some specific bifurcation properties, such as direction, stability, and period. Furthermore, by examining a model with constant coefficients, we also analyze how diffusion and the amount of time needed for prey to mature impact the model's dynamics. To support the obtained analytical results, we also run some numerical simulations. The results indicate that the dynamic of the mathematical model is significantly influenced by diffusion, the amount of time needed for the predator to gain the capacity to hunt, and the amount of time required for prey to reach maturity that the predator can hunt.
  • Article
    Citation - WoS: 103
    Citation - Scopus: 107
    Some Novel Mathematical Analysis on the Fractal-Fractional Model of the Ah1n1/09 Virus and Its Generalized Caputo-Type Version
    (Pergamon-elsevier Science Ltd, 2022) Avci, Ibrahim; Kumar, Pushpendra; Baleanu, Dumitru; Rezapour, Shahram; Etemad, Sina
    In this paper, we formulate a new model of a particular type of influenza virus called AH1N1/09 in the framework of the four classes consisting of susceptible, exposed, infectious and recovered people. For the first time, we here investigate this model with the help of the advanced operators entitled the fractal-fractional operators with two fractal and fractional orders via the power law type kernels. The existence of solution for the mentioned fractal-fractional model of AH1N1/09 is studied by some special mappings such as ?-psi-contractions and ?-admissibles. The Leray-Schauder theorem is also applied for this aim. After investigating the stability criteria in four versions, to approximate the desired numerical solutions, we implement Adams-Bashforth (AB) scheme and simulate the graphs for different data on the fractal and fractional orders. Lastly, we convert our fractal-fractional AH1N1/09 model into a fractional model via the generalized Liouville-Caputo-type (GLC-type) operators and then, we simulate new graphs caused by the new numerical scheme called Kumar-Erturk method.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 19
    Results on Hilfer Fractional Switched Dynamical System With Non-Instantaneous Impulses
    (indian Acad Sciences, 2022) Malik, Muslim; Baleanu, Dumitru; Kumar, Vipin
    This paper concerns with the existence, uniqueness, Ulam's Hyer (UH) stability and total controllability results for the Hilfer fractional switched impulsive systems in finite-dimensional spaces. Mainly, this paper can be divided into three parts. In the first part, we examine the existence of a unique solution. In the second part, we establish the UH stability results, and in the third part, we study the total controllability results. The main outcomes are acquired by utilising the nonlinear analysis, fractional calculus, Mittag-Leffler function and Banach contraction principle. Finally, we have given two examples to validate the obtained analytical results.
  • Conference Object
    Citation - Scopus: 1
    Modeling and Analysis of Smokers Model With Constant Proportional Fractional Operators
    (Institute of Electrical and Electronics Engineers Inc., 2023) Baleanu, D.; Farman, M.
    Despite the existence of a secure environment, smoke subjection continues to be a leading cause of serious illness globally. For investigation and observation of the dynamical transmission of the smoker, we examine a fractional order smoker model with Constant Proportional Atangana-Baleanu (in Caputo sense) operator. We treated the proposed model's positivity, boundedness, well-posedness and stability analysis of the model. There is a brief discussion of additional analysis on CPABC operators. Using the Laplace Adomian Decomposition Method, we simulate a system of fractional differential equations numerically. This model's tools seem to be quite strong and capable of reproducing the issue's anticipated theoretical conditions. © 2023 IEEE.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 9
    Numerical Simulation for Generalized Time-Fractional Burgers' Equation With Three Distinct Linearization Schemes
    (Asme, 2023) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Chawla, Reetika; Reetika, Chawla
    In the present study, we examined the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative by adopting the Atangana-Baleanu Caputo derivative. A stability analysis of the linearized time-fractional Burgers' difference equation was also presented. All linearization strategies used to solve the proposed nonlinear problem are unconditionally stable. To support the theory, two numerical examples are considered. Furthermore, numerical results demonstrate the comparison of linearization strategies and manifest the effectiveness of the proposed numerical scheme in three distinct ways.
  • Article
    Citation - WoS: 22
    Citation - Scopus: 30
    Global Stability Results for Volterra-Hadamard Random Partial Fractional Integral Equations
    (Springer-verlag Italia Srl, 2023) Abbas, Said; Benchohra, Mouffak; Karapinar, Erdal; Salim, Abdelkrim
    This paper investigates the existence and stability of random solutions of a class of Hadamard fractional order functional partial integral equations with random effects in Banach spaces.
  • Article
    Citation - WoS: 107
    Citation - Scopus: 107
    Dynamics Exploration for a Fractional-Order Delayed Zooplankton-Phytoplankton System
    (Pergamon-elsevier Science Ltd, 2023) Gao, Rong; Xu, Changjin; Li, Ying; Akgul, Ali; Baleanu, Dumitru; Li, Peiluan
    In this study, we are concerned with the dynamics of a new established fractional-order delayed zooplankton- phytoplankton system. The existence and uniqueness of the solution are proved via Banach fixed point theorem. Non-negativeness of the solution is studied by mathematical inequality technique. The boundedness of the solution is analyzed by virtue of constructing an appropriate function. A novel delay-independent sufficient condition ensuring the stability and the onset of Hopf bifurcation for the established fractional -order delayed zooplankton-phytoplankton system is derived by means of Laplace transform, stability criterion and bifurcation knowledge of fractional-order differential equation. The global stability condition for the involved fractional-order delayed zooplankton-phytoplankton system is built by using a suitable positive definite function. Taking advantage of hybrid control tactics, we effectively control the time of occurrence of Hopf bifurcation for the established fractional-order delayed zooplankton-phytoplankton system. The study manifests that delay plays a vital role in controlling the stability and the time of occurrence of Hopf bifurcation for the involved fractional-order delayed zooplankton-phytoplankton system and the fractional -order controlled zooplankton-phytoplankton system involving delays. To verify the correctness of established chief results, computer simulation figures are distinctly displayed. The derived conclusions of this research are entirely new and possess potential theoretical value in preserving the balance of biological population. Up to now, there are few publications on detailed and comprehensive dynamic analysis on fractional-order delayed zooplankton-phytoplankton system via various exploration ways.