Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 42Citation - Scopus: 44A Numerical Approach for Solving Fractional Optimal Control Problems With Mittag-Leffler Kernel(Sage Publications Ltd, 2022) Ganji, Roghayeh M.; Sayevand, Khosro; Baleanu, Dumitru; Jafari, HosseinIn this work, we present a numerical approach based on the shifted Legendre polynomials for solving a class of fractional optimal control problems. The derivative is described in the Atangana-Baleanu derivative sense. To solve the problem, operational matrices of AB-fractional integration and multiplication, together with the Lagrange multiplier method for the constrained extremum, are considered. The method reduces the main problem to a system of nonlinear algebraic equations. In this framework by solving the obtained system, the approximate solution is calculated. An error estimate of the numerical solution is also proved for the approximate solution obtained by the proposed method. Finally, some illustrative examples are presented to demonstrate the accuracy and validity of the proposed scheme.Conference Object Citation - WoS: 38Citation - Scopus: 48Analysis of Keller-Segel Model With Atangana-Baleanu Fractional Derivative(Univ Nis, Fac Sci Math, 2018) Baleanu, Dumitru; Celik, Ercan; Dokuyucu, Mustafa AliThe new definition of the fractional derivative was defined by Atangana and Baleanu in 2016. They used the generalized Mittag-Leffler function with the non-singular and non-local kernel. Further, their version provides all properties of fractional derivatives. Our aim is to analyse the Keller-Segel model with Caputo and Atangana-Baleanu fractional derivative in Caputo sense. Using fixed point theory, we first show the existence of coupled solutions. We then examine the uniqueness of these solutions. Finally, we compare our results numerically by modifying our model according to both definitions, and we demonstrate these results on the graphs in detail. All computations were done using Mathematica.Article Citation - WoS: 201Citation - Scopus: 209Analysis of Regularized Long-Wave Equation Associated With a New Fractional Operator With Mittag-Leffler Type Kernel(Elsevier, 2018) Singh, Jagdev; Baleanu, Dumitru; Sushila; Kumar, DevendraIn this work, we aim to present a new fractional extension of regularized long-wave equation. The regularized long-wave equation is a very important mathematical model in physical sciences, which unfolds the nature of shallow water waves and ion acoustic plasma waves. The existence and uniqueness of the solution of the regularized long-wave equation associated with Atangana Baleanu fractional derivative having Mittag-Leffler type kernel is verified by implementing the fixed-point theorem. The numerical results are derived with the help of an iterative algorithm. In order to show the effects of various parameters and variables on the displacement, the numerical results are presented in graphical and tabular form. (C) 2017 Elsevier B.V. All rights reserved.Article Citation - WoS: 4Analysis of Drude Model Using Fractional Derivatives Without Singular Kernels(de Gruyter Open Ltd, 2017) Rosales Garcia, J. Juan; Ortega Contreras, Abraham; Baleanu, Dumitru; Martinez Jimenez, LeonardoWe report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF), and fractional derivatives with a stretched Mittag-Leffer function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < gamma <= 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when gamma < 0.8.