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: 20Citation - Scopus: 20Computational Results With Non-Singular and Non-Local Kernel Flow of Viscous Fluid in Vertical Permeable Medium With Variant Temperature(Frontiers Media Sa, 2020) Saeed, Syed T.; Baleanu, Dumitru; Ghalib, Muhammad M.; Riaz, Muhammad B.This present article explores the transversal magnetized flow of a viscous fluid. The flow is confined to a vertical wall, saturated in permeable medium, along with ramped wall temperature. In this study, the conjugate impact of heat and mass transfer with slip and non-slip conditions are considered in the velocity field and energy equation. The dimensionless Atangana-Baleanu fractional governing equations are derived with Laplace transformation. Computational results are expressed graphically with the effect of various physical parameters. Comparative graphical analysis of the Atangana-Baleanu derivative for temperature, concentration and velocity field, with slip and non-slip impact, shows that the memory effects of the Atangana-Baleanu derivative are better than the results that exist in the literature.Article Citation - WoS: 15Citation - Scopus: 18New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices(Asme, 2019) Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; Yousef, FerasHerein, analytical solutions of three-dimensional (3D) diffusion, telegraph, and Burgers' models that are equipped with three memory indices are derived by using an innovative fractional generalization of the traditional differential transform method (DTM), namely, the threefold-fractional differential transform method (threefold-FDTM). This extends the applicability of DTM to comprise initial value problems in higher fractal spaces. The obtained solutions are expressed in the form of a (gamma) over bar -fractional power series which is a fractional adaptation of the classical Taylor series in several variables. Furthermore, the projection of these solutions into the integer space corresponds with the solutions of the classical copies for these models. The results detect that the suggested method is easy to implement, accurate, and very efficient in (non)linear fractional models. Thus, research on this trend is worth tracking.Article Citation - WoS: 173Citation - Scopus: 173On the Fractional Optimal Control Problems With a General Derivative Operator(Wiley, 2021) Baleanu, Dumitru; Jajarmi, AminThis paper deals with a general form of fractional optimal control problems involving the fractional derivative with singular or non-singular kernel. The necessary conditions for the optimality of these problems are derived and a new numerical method is designed to solve these equations effectively. Simulation results indicate that the proposed method works well and provides satisfactory results with regard to accuracy and computational effort. Comparative results also verify that a particular case with Mittag-Leffler kernel improves the performance of the controlled system in terms of the transient response compared to the other fractional- and integer-order derivatives.Article Citation - WoS: 132Citation - Scopus: 154The Fractional Features of a Harmonic Oscillator With Position-Dependent Mass(Iop Publishing Ltd, 2020) Jajarmi, Amin; Sajjadi, Samaneh Sadat; Asad, Jihad H.; Baleanu, DumitruIn this study, a harmonic oscillator with position-dependent mass is investigated. Firstly, as an introduction, we give a full description of the system by constructing its classical Lagrangian; thereupon, we derive the related classical equations of motion such as the classical Euler-Lagrange equations. Secondly, we fractionalize the classical Lagrangian of the system, and then we obtain the corresponding fractional Euler-Lagrange equations (FELEs). As a final step, we give the numerical simulations corresponding to the FELEs within different fractional operators. Numerical results based on the Caputo and the Atangana-Baleanu-Caputo (ABC) fractional derivatives are given to verify the theoretical analysis.Article Citation - WoS: 174Citation - Scopus: 199A New Fractional Modelling and Control Strategy for the Outbreak of Dengue Fever(Elsevier, 2019) Arshad, Sadia; Baleanu, Dumitru; Jajarmi, AminThis paper deals with a new mathematical model for a dengue fever outbreak based on a system of fractional differential equations. The equilibrium points and stability of the new system are studied. To simulate this model, a new and efficient numerical method is provided and its stability and convergence are proved. According to a real outbreak on the Cape Verde Islands occurred in year 2009, the new model is examined for a period of three months by using singular or nonsingular kernels in the definition of derivative operator. Simulation results show that the proposed formalism with exponential kernel agrees well with the real data in the early stage of the epidemic while the Mittag-Leffler kernel fits the reality for the later part of the time interval. Hence, the new framework in a hybrid manner can properly simulate the dynamics of the disease in the whole of the time interval. In order to stabilize the disease-free equilibrium point of the system under investigation, two control strategies are suggested. Numerical simulations verify that the proposed stabilizing controllers are efficient and provide significantly remarkable results. (C) 2019 Elsevier B.V. All rights reserved.Article Citation - WoS: 20Citation - Scopus: 26Homotopy Analysis Method for Solving Abel Differential Equation of Fractional Order(de Gruyter Poland Sp Z O O, 2013) Sayevand, Khosro; Tajadodi, Haleh; Baleanu, Dumitru; Jafari, HosseinIn this study, the homotopy analysis method is used for solving the Abel differential equation with fractional order within the Caputo sense. Stabilityand convergence of the proposed approach is investigated. The numerical results demonstrate that the homotopy analysis method is accurate and readily implemented.Article Citation - WoS: 42Citation - Scopus: 48A Novel Analytical Technique for the Solution of Time-Fractional Ivancevic Option Pricing Model(Elsevier, 2020) Chakraverty, Snehashish; Baleanu, Dumitru; Jena, Rajarama MohanThe Ivancevic option pricing model is an alternative of the standard Black-Scholes pricing equation, which signifies a controlled Brownian motion related to the nonlinear Schrodinger equation. Even though many researchers have studied the applicability and practicality of this model, but the analytical approach of this model is rarely found in the literature. In this paper, a novel semi-analytical technique called fractional reduced differential transform method has been applied to solve the Schrodinger type option pricing model, which is characterized by the time-fractional derivative. Two problems are explained to validate and prove the effectiveness of the proposed technique. Obtained results are compared with the solution of other existing methods for a particular case. This comparison shows that the attained results are in good agreement with the existing solutions. (C) 2020 Published by Elsevier B.V.Article Citation - WoS: 100Citation - Scopus: 123A New Feature of the Fractional Euler-Lagrange Equations for a Coupled Oscillator Using a Nonsingular Operator Approach(Frontiers Media Sa, 2019) Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Asad, Jihad H.; Jajarmi, AminIn this new work, the free motion of a coupled oscillator is investigated. First, a fully description of the system under study is formulated by considering its classical Lagrangian, and as a result, the classical Euler-Lagrange equations of motion are constructed. After this point, we extend the classical Lagrangian in fractional sense, and thus, the fractional Euler-Lagrange equations of motion are derived. In this new formulation, we consider a recently introduced fractional operator with Mittag-Leffler non-singular kernel. We also present an efficient numerical method for solving the latter equations in a proper manner. Due to this new powerful technique, we are able to obtain remarkable physical thinks; indeed, we indicate that the complex behavior of many physical systems is realistically demonstrated via the fractional calculus modeling. Finally, we report our numerical findings to verify the theoretical analysis.