Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 111Citation - Scopus: 123Stability Analysis and System Properties of Nipah Virus Transmission: a Fractional Calculus Case Study(Pergamon-elsevier Science Ltd, 2023) Shekari, Parisa; Torkzadeh, Leila; Ranjbar, Hassan; Jajarmi, Amin; Nouri, Kazem; Baleanu, DumitruIn this paper, we establish a Caputo-type fractional model to study the Nipah virus transmission dynamics. The model describes the impact of unsafe contact with an infectious corpse as a possible way to transmit this virus. The corresponding area to the system properties, including the positivity and boundedness of the solution, is explored by using the generalized fractional mean value theorem. Also, we investigate sufficient conditions for the local and global stability of the disease-free and the endemic steady-states based on the basic reproduction number R0. To show these important stability features, we employ fractional Routh-Hurwitz criterion and LaSalle's invariability principle. For the implementation of this epidemic model, we also use the Adams-Bashforth-Moulton numerical method in a fractional sense. Finally, in addition to compare the fractional and classical results, as one of the main goals of this research, we demonstrate the usefulness of minimal unsafe touch with the infectious corpse. Simulation and comparative results verify the theoretical discussions.Article Citation - WoS: 36Citation - Scopus: 36All Linear Fractional Derivatives With Power Functions' Convolution Kernel and Interpolation Properties(Pergamon-elsevier Science Ltd, 2023) Baleanu, Dumitru; Shiri, BabakOur attempt is an axiomatic approach to find all classes of possible definitions for fractional derivatives with three axioms. In this paper, we consider a special case of linear integro-differential operators with power functions' convolution kernel a(a)(t-s)b(a) of order a a (0,1). We determine analytic functions a(a) and b(a) such that when a-* 0+, the corresponding operator becomes identity operator, and when a-* 1- the corresponding operator becomes derivative operator. Then, a sequential operator is used to extend the fractional operator to a higher order. Some properties of the sequential operator in this regard also are studied. The singularity properties, Laplace transform and inverse of the new class of fractional derivatives are investigated. Several examples are provided to confirm theoretical achievements. Finally, the solution of the relaxation equation with diverse fractional derivatives is obtained and compared.Article Citation - WoS: 33Citation - Scopus: 35Nonlinear F-Contractions on B-Metric Spaces and Differential Equations in the Frame of Fractional Derivatives With Mittag-Leffler Kernel(Pergamon-elsevier Science Ltd, 2019) Jarad, Fahd; Karapinar, Erdal; Alqahtani, Badr; Fulga, AndreeaIn this manuscript, we aim to refine and characterize nonlinear F-contractions in a more general framework of b-metric spaces. We investigate the existence and uniqueness of such contractions in this setting. We discuss the solutions to differential equations in the setting of fractional derivatives involving Mittag-Leffler kernels (Atangana-Baleanu fractional derivative) by using nonlinear F-contractions that indicate the genuineness of the presented result. (C) 2019 Elsevier Ltd. All rights reserved.Article Citation - WoS: 716Citation - Scopus: 762A New Study on the Mathematical Modelling of Human Liver With Caputo-Fabrizio Fractional Derivative(Pergamon-elsevier Science Ltd, 2020) Jajarmi, Amin; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, DumitruIn this research, we aim to propose a new fractional model for human liver involving Caputo-Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard-Lindelof approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the results. Comparative results with the real clinical data indicate the superiority of the new fractional model over the pre-existent integer-order model with ordinary time-derivatives. (C) 2020 Elsevier Ltd. All rights reserved.Article Citation - WoS: 134Citation - Scopus: 154A New Approach for Solving Multi Variable Orders Differential Equations With Mittag-Leffler Kernel(Pergamon-elsevier Science Ltd, 2020) Jafari, H.; Baleanu, D.; Ganji, R. M.In this paper we consider multi variable orders differential equations (MVODEs) with non-local and no-singular kernel. The derivative is described in Atangana and Baleanu sense of variable order. We use the fifth-kind Chebyshev polynomials as basic functions to obtain operational matrices. We transfer the original equations to a system of algebraic equations using operational matrices and collocation method. The convergence analysis of the presented method is discussed. Few examples are presented to show the efficiency of the presented method. (C) 2019 Elsevier Ltd. All rights reserved.Article Citation - WoS: 15Citation - Scopus: 18Existence of a Periodic Mild Solution for a Nonlinear Fractional Differential Equation(Pergamon-elsevier Science Ltd, 2012) Baleanu, Dumitru; Herzallah, Mohamed A. E.; Mohammadzadeh, B.; Darzi, R.; Neamaty, A.The aim of this manuscript is to analyze the existence of a periodic mild solution to the problem of the following nonlinear fractional differential equation (R)(0)D(t)(alpha)u(t) - lambda u(t) = f(t, u(t)), u(0) = u(1) = 0, 1 < alpha < 2, lambda is an element of R, where D-R(0)t(alpha), denotes the Riemann-Liouville fractional derivative. We obtained the expressions of the general solution for the linear fractional differential equation by making use of the Laplace and inverse Laplace transforms. By making use of the Banach contraction mapping principle and the Schaefer fixed point theorem, the existence results of one or at least one mild solution for a nonlinear fractional differential equation were given. (C) 2011 Elsevier Ltd. All rights reserved.Article Citation - WoS: 199Citation - Scopus: 217A New Fractional Analysis on the Interaction of Hiv With Cd4<sup>+</Sup> T-Cells(Pergamon-elsevier Science Ltd, 2018) Baleanu, Dumitru; Jajarmi, AminMathematical modeling of biological systems is an interesting research topic that attracted the attention of many researchers. One of the main goals in this area is the design of mathematical models that more accurately illustrate the characteristics of the real-world phenomena. Among the existing research projects, modeling of immune systems has given a growing attention due to its natural capabilities in identifying and destroying abnormal cells. The main objective of this paper is to investigate the pathological behavior of HIV-infection using a new model in fractional calculus. The proposed model is examined through three different operators of fractional derivatives. An efficient numerical method is also presented to solve these fractional models effectively. In fact, we believe that the new models presented on the basis of these three operators show various asymptomatic behaviors that do not appear during the modeling with the integer-order derivatives. Therefore, the fractional calculus provides more precise models of biological systems that help us to make more realistic judgments about their complex dynamics. Finally, simulations results are provided to confirm the theoretical analysis. (C) 2018 Elsevier Ltd. All rights reserved.Article Citation - WoS: 50Citation - Scopus: 64New Studies for General Fractional Financial Models of Awareness and Trial Advertising Decisions(Pergamon-elsevier Science Ltd, 2017) Abou Hasan, Muner M.; Baleanu, Dumitru; Sweilam, Nasser H.In this paper, two numerical techniques are introduced to study numerically the general fractional advertising model. This system describes the flux of the consumers from unaware individuals group to aware or purchased group. The first technique is an asymptotically stable difference scheme, which was structured depending on the nonstandard finite difference method. This scheme preserves the properties of the solutions of the model problem as the positivity and the boundedness. The second technique is the Jacobi-Gauss-Lobatto spectral collocation method which is exponentially accurate. By means of this approach, such problem is reduced to solve a system of nonlinear algebraic equations and are greatly simplified the problem. Numerical comparisons to test the behavior of the used techniques are run out. We conclude from the computational work that: the Jacobi-Gauss-Lobatto spectral collocation method is more accurate whereas the nonstandard finite difference method requires less computational time. (C) 2017 Elsevier Ltd. All rights reserved.Article Citation - WoS: 94Citation - Scopus: 104New Aspects of the Adaptive Synchronization and Hyperchaos Suppression of a Financial Model(Pergamon-elsevier Science Ltd, 2017) Hajipour, Mojtaba; Baleanu, Dumitru; Jajarmi, AminThis paper mainly focuses on the analysis of a hyperchaotic financial system as well as its chaos control and synchronization. The phase diagrams of the above system are plotted and its dynamical behaviours like equilibrium points, stability, hyperchaotic attractors and Lyapunov exponents are investigated. In order to control the hyperchaos, an efficient optimal controller based on the Pontryagin's maximum principle is designed and an adaptive controller established by the Lyapunov stability theory is also implemented. Furthermore, two identical financial models are globally synchronized by using an interesting adaptive control scheme. Finally, a fractional economic model is introduced which can also generate hyperchaotic attractors. In this case, a linear state feedback controller together with an active control technique are used in order to control the hyperchaos and realize the synchronization, respectively. Numerical simulations verifying the theoretical analysis are included. (C) 2017 Elsevier Ltd. All rights reserved.