Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Conference Object Citation - Scopus: 5About Fractional Calculus of Singular Lagrangians(Institute of Electrical and Electronics Engineers Inc., 2004) Baleanu, D.; Baleanu, D.In this paper the solutions of the fractional Euler-Lagrange equations corresponding to singular fractional Lagrangians were examined. Despite of the complexity of solutions in the fractional case the gauge classical symmetry was preserved. Four examples of fractional singular Lagrangians were analyzed in details. © 2004 IEEE.Conference Object Citation - Scopus: 1A Fractional Lagrangian Approach for Two Masses With Linear and Cubic Nonlinear Stiffness(Institute of Electrical and Electronics Engineers Inc., 2023) Baleanu, D.; Jajarmi, A.; Wannan, R.; Asad, J.; Defterli, O.In this manuscript, the fractional dynamics of the two-mass spring system with two kinds of stiffness, namely linear and strongly nonlinear, are investigated. The corresponding fractional Euler-Lagrange equations of the system are derived being a system of two-coupled fractional differential equations with strong cubic nonlinear term. The numerical results of the system are obtained using Euler's approximation method and simulated with respect to the different values of the model parameters as mass, stiffness and order of the fractional derivative in use. The interpretation of the approximate results of the so-called generalized two-mass spring system is discussed via the fractional order. © 2023 IEEE.Conference Object Citation - Scopus: 2Multicompartmental Mathematical Models of Infectious Dynamic Diseases With Time Fractional-Order Derivatives(Institute of Electrical and Electronics Engineers Inc., 2023) Baleanu, D.; Rahman, M.U.; Momani, S.; Karaca, Y.Nonlinear dynamic models with multiple compartments are characterized by subtle attributes like high dimensionality and heterogeneity, with fractional-order derivatives and constituting fractional calculus, which can provide a thorough comprehension, control and optimization of the related dynamics and structure. This requirement poses a formidable challenge, and thereby, has gained prominence in different fields where fractional derivatives and nonlinearities interact. Thus, fractional models have become relevant to address phenomena with memory effects, with fractional calculus providing amenities to deal with the time-dependent impacts observed. A novel infectious disease epidemic model with time fractional order and a Caputo fractional derivative type operator is discussed in the current study which is carried out for the considered epidemic model. Accordingly, a method for the semi-analytical solution of the epidemic model of a dynamic infectious disease with fractional order is employed in terms of the Caputo fractional derivative operator in this study. The existence and uniqueness of the solution is constructed with the aid of fixed point theory in particular. Furthermore, the Adams-Bashforth method, an extensively employed technique for the semi-analytical solution of these types of models. The simulation results for various initial data demonstrate that the solution of the considered model is stable and shows convergence toward a single point, and numerical simulations for different fractional orders lying between (0,1) and integer order have been obtained. On both initial approximations, the dynamical behavior of each compartment has shown stability as well as convergence. Consequently, the results obtained from our study based on experimental data can be stated to confirm the accurate total density and capacity for each compartment lying between two different integers considering dynamical processes and systems. © 2023 IEEE.Conference Object Citation - Scopus: 3K-Symbol Atangana-Baleanu Fractional Operators in a Complex Domain(Institute of Electrical and Electronics Engineers Inc., 2023) Baleanu, D.; Ibrahim, R.W.; Momani, S.The majority of research on fractional differential operators focuses on functions of real variables. Atangana-Baleanu fractional differential operators (AB-fractional differential operators) are formulated in this study for a class of normalized analytic functions in the open unit disk. The recommended operators are looked at using geometric function theory principles. © 2023 IEEE.Conference Object A General Form of Fractional Derivatives for Modelling Purposes in Practice(Institute of Electrical and Electronics Engineers Inc., 2023) Baleanu, D.; Jajarmi, A.In this paper, we propose new mathematical models for the complex dynamics of the world population growth as well as a human body's blood ethanol concentration by using a general formulation in fractional calculus. In these new models, we employ a recently introduced ψ-Caputo fractional derivative whose kernel is defined based on another function. Meanwhile, a number of comparative experiences are carried out in order to verify the models according to some sets of real data. Simulation results indicate that better approximations are achieved when the systems are modeled by using the new general fractional formulation than the other cases of fractional- and integer-order descriptions. © 2023 IEEE.Conference Object Citation - Scopus: 1Modeling 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.