Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 6Citation - Scopus: 6On Modeling the Groundwater Flow Within a Confined Aquifer(Editura Acad Romane, 2015) Atangana, Abdon; Baleanu, Dumitru; Baleanu, Dumitru; MatematikThe groundwater flow equation is used to simulate the movement of water under the confined aquifer. In this paper we study a modification of the groundwater flow equation within a newly proposed derivative. We numerically solve the generalized groundwater flow equation with the Crank-Nicholson scheme. We also analytically solve the generalized equation via the method of separation of variable.Article Citation - WoS: 69Citation - Scopus: 73Classical and Fractional Aspects of Two Coupled Pendulums(Editura Acad Romane, 2019) Baleanu, D.; Baleanu, Dumitru; Jajarmi, A.; Asad, J. H.; MatematikIn this study, we consider two coupled pendulums (attached together with a spring) having the same length while the same masses are attached at their ends. After setting the system in motion we construct the classical Lagrangian, and as a result, we obtain the classical Euler-Lagrange equation. Then, we generalize the classical Lagrangian in order to derive the fractional Euler-Lagrange equation in the sense of two different fractional operators. Finally, we provide the numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on the Euler method to discretize the convolution integral. Numerical simulations show that the proposed approach is efficient and demonstrate new aspects of the real-world phenomena.Article Citation - WoS: 67Citation - Scopus: 69The Fractional Model of Spring Pendulum: New Features Within Different Kernels(Editura Acad Romane, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; MatematikIn this work, new aspects of the fractional calculus (FC) are examined for a model of spring pendulum in fractional sense. First, we obtain the classical Lagrangian of the model, and as a result, we derive the classical Euler-Lagrange equations of the motion. Second, we generalize the classical Lagrangian to fractional case and derive the fractional Euler-Lagrange equations in terms of fractional derivatives with singular and nonsingular kernels, respectively. Finally, we provide the numerical solution of these equations within two fractional operators for some fractional orders and initial conditions. Numerical simulations verify that taking into account the recently features of the FC provides more realistic models demonstrating hidden aspects of the real-world phenomena.Book Part Citation - WoS: 25Citation - Scopus: 1New Treatise in Fractional Dynamics(Springer-verlag Berlin, 2012) Baleanu, Dumitru; Baleanu, DumitruFractional calculus becomes a powerful tool used to investigate complex phenomena from various fields of science and engineering. In this context, the researchers paid a lot of attention for the fractional dynamics. However, the fractional modeling is still at the beginning of its developing. The aim of this chapter is to present some new results in the area of fractional dynamics and its applications.Article Citation - WoS: 98Citation - Scopus: 112Analysis and Some Applications of a Regularized Ψ-Hilfer Fractional Derivative(Elsevier, 2022) Jajarmi, Amin; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Nieto, Juan J.The main purpose of this research is to present a generalization of Psi-Hilfer fractional derivative, called as regularized Psi-Hilfer, and study some of its basic characteristics. In this direction, we show that the psi-Riemann-Liouville integral is the inverse operation of the presented regularized differentiation by means of the same function psi. In addition, we consider an initial-value problem comprising this generalization and analyze the existence as well as the uniqueness of its solution. To do so, we first present an approximation sequence via a successive substitution approach; then we prove that this sequence converges uniformly to the unique solution of the regularized Psi-Hilfer fractional differential equation (FDE). To solve this FDE, we suggest an efficient numerical scheme and show its accuracy and efficacy via some real-world applications. Simulation results verify the theoretical consequences and show that the regularized Psi-Hilfer fractional mathematical system provides a more accurate model than the other kinds of integer- and fractional-order differential equations. (C) 2022 Elsevier B.V. All rights reserved.Article Citation - WoS: 15Citation - Scopus: 23Optical Solitons With Nonlinear Dispersion in Parabolic Law Medium and Three-Component Coupled Nonlinear Schrodinger Equation(Springer, 2022) Sulaiman, Tukur Abdulkadir; Alshomrani, Ali S.; Baleanu, Dumitru; Yusuf, AbdullahiThe current study looks at two different nonlinear Schrodinger equations. These equations have several applications in science and engineering, such as nonlinear fiber optics, electromagnetic field waves, and signal processing via optical fibers. In this study, we investigate these equations using an efficient integration strategy known as complex envelop antazs. As a result, we obtain novel solutions such as bright, dark, and combined dark-bright soliton solutions. Important physical aspects have been depicted in three dimensions and contour plots for clear interpretation of the acquired solutions.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: 15Citation - Scopus: 18A New Fractional Sica Model and Numerical Method for the Transmission of Hiv/Aids(Wiley, 2021) Baleanu, Dumitru; Ullah, Malik Zaka; Zaka Ullah, MalikIn this research, a new SICA model is proposed in a fractional framework for the HIV/AIDS transmission dynamics. The new model involves a Caputo-type fractional derivative with a Mittag-Leffler function as its nonsingular kernel. In addition, the resultant fractional equations avoid dimensional mismatching by using an auxiliary parameter. Furthermore, the nonnegativity of the solution, the equilibrium points, and their stability are studied. Additionally, we implement the model by a powerful approximation scheme based on the product-integration rule. Comparative results with the real experimental observations, happened in Cape Verde Islands from 1987 to 2014, verify that the new fractional model is more efficient than the pre-existent classical model with ordinary time derivatives. More to the point, the fractional order itself provides a degree of flexibility affecting the performance of the model, which is helpful to exhibit the hidden features of the disease transmission in an accurate, appropriate manner.Conference Object Path Integral Quantization of Brownian Motion as Mechanical Systems With Fractional Derivatives(IFAC Secretariat, 2006) Rabei, E.M.; Baleanu, D.; Muslih, S.I.In this paper, the mechanical systems with fractional derivatives are studied by using fractional formalism. The path integral quantization of these system is constructed as an integration over the canonical phase space. The path integral quantization of a system with Brownian motion is carried out. Copyright 2006 IFAC.