Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Conference Object Nonconservative Systems Within Fractional Generalized Derivatives(IFAC Secretariat, 2006) Baleanu, D.; Muslih, S.I.Fractional calculus is a promising tool for investigation of both conservative and non-conservative systems. Fractional Hamiltonian formulation represents an important problem of the fractional quantization. In this paper the nonconservative Lagrangian mechanics is investigated within fractional generalized derivative approach.Article Magnetic Stimulation on Human Blood :electromotive Force Analysis(SYSCOM 18 S.R.L., 2018) Fraga, T.C.; Magdaleno, D.M.; Gómez-Aguilar, J.F.; Murillo, B.O.; Sosa, M.; Baleanu, D.; Cabrera, R.G.In this work a comparative theoretical analysis vs. experimental study on human blood under a magnetic field stimulation is presented. Twenty samples of leukoreduced human blood were stimulated with an alternant magnetic field using a Helmholtz coil system; this magnetic field induced an electromotive force in them. Theoretical calculations were performed for the induced electromotive force in a simple model of blood tissue under magnetic stimulation at frequencies: 50 Hz, 100 Hz, 800 Hz, and 1500 Hz. Experimental measurement was performed at the same frequencies for comparison purposes. Results show a high correlation between theoretical and experimental study, as well as effects of agglutination in the stimulated blood cells. © 2018 SYSCOM 18 S.R.L. All Rights Reserved.Conference Object Citation - WoS: 5Citation - Scopus: 6Fractional Differentiation and Its Applications (Fda08)(Iop Publishing Ltd, 2009) Baleanu, D.; Tenreiro Machado, J.A.The international workshop, Fractional Differentiation and its Applications (FDA08), held at Cankaya University, Ankara, Turkey on 5-7 November 2008, was the third in an ongoing series of conferences dedicated to exploring applications of fractional calculus in science, engineering, economics and finance. Fractional calculus, which deals with derivatives and integrals of any order, is now recognized as playing an important role in modeling multi-scale problems that span a wide range of time or length scales. Fractional calculus provides a natural link to the intermediate-order dynamics that often reflects the complexity of micro- and nanostructures through fractional-order differential equations. Unlike the more established techniques of mathematical physics, the methods of fractional differentiation are still under development; while it is true that the ideas of fractional calculus are as old as the classical integer-order differential operators, modern work is proceeding by both expanding the capabilities of this mathematical tool and by widening its range of applications. Hence, the interested reader will find papers here that focus on the underlying mathematics of fractional calculus, that extend fractional-order operators into new domains, and that apply well established methods to experimental and theoretical problems. The organizing committee invited presentations from experts representing the international community of scholars in fractional calculus and welcomed contributions from the growing number of researchers who are applying fractional differentiation to complex technical problems. The selection of papers in this topical issue of Physica Scripta reflects the success of the FDA08 workshop, with the emergence of a variety of novel areas of application. With these ideas in mind, the guest editors would like to honor the many distinguished scientists that have promoted the development of fractional calculus and, in particular, Professor George M Zaslavsky who supported this special issue but passed away recently. The organizing committee wishes to thank the sponsors and supporters of FDA08, namely Cankaya University represented by the President of the Board of Trustees Sitki Alp and Rector Professor Ziya B Güvenc, The Scientfic and Technological Research Council of Turkey (TUBITAK) and the IFAC for providing the resources needed to hold the workshop, the invited speakers for sharing their expertise and knowledge of fractional calculus, and the participants for their enthusiastic contributions to the discussions and debates. © 2009 The Royal Swedish Academy of Sciences.Article Citation - Scopus: 25On the Geometric and Physical Properties of Conformable Derivative(Murat TOSUN, 2024) Has, A.; Yılmaz, B.; Baleanu, D.In this article, we explore the advantages geometric and physical implications of the conformable derivative. One of the key benefits of the conformable derivative is its ability to approximate the tangent at points where the classical tangent is not readily available. By employing conformable derivatives, alternative tangents can be created to overcome this limitation. Thanks to these alternative (conformable) tangents, physical interpretation can be made with alternative velocity vectors. Furthermore, the conformable derivative proves to be valuable in situations where the tangent plane cannot be defined. It enables the creation of alternative tangent planes, offering a solution in cases where the traditional approach falls short. Geometrically speaking, the conformable derivative carries significant meaning. It provides insights into the local behavior of a function and its relationship with nearby points. By understanding the conformable derivative, we gain a deeper understanding of how a function evolves and changes within its domain. A several examples are presented in the article to better understand the article and visualize the concepts discussed. These examples are accompanied by visual representations generated using the Mathematica program, aiding in a clearer understanding of the proposed ideas. By combining theoretical explanations, practical examples, and visualizations, this article aims to provide a comprehensive exploration of the advantages and geometric and physical implications of the conformable derivative. © MSAEN.Article Citation - Scopus: 11A Mathematical Theoretical Study of Atangana-Baleanu Fractional Burgers’ Equations(Elsevier B.V., 2024) Baleanu, D.; Jassim, H.K.; Ahmed, H.; Singh, J.; Kumar, D.; Shah, R.; Jabbar, K.A.In this paper, the Burgers’ equations using the fractional derivative of Atangana-Baleanu sense are investigated and discussed. A Laplace variational iteration approach is used to demonstrate the fractional model's mathematical solution. The solution's existence and uniqueness are examined using fixed point theory. Several numerical simulations that enhance the efficacy of the employed derivative are presented and discussed. © 2024Editorial Guest Editors(Taru Publications, 2022) Singh, J.; Kumar, D.; Baleanu, D.Erratum Erratum: Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems With Delay (Abstract and Applied Analysis)(2011) Sadati, S.J.; Baleanu, D.; Ranjbar, A.; Ghaderi, R.; Abdeljawad Maraaba, T.Article Citation - WoS: 8Citation - Scopus: 35A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line(Hindawi Ltd, 2013) Baleanu, D.; Bhrawy, A. H.; Taha, T. M.This paper deals with modified generalized Laguerre spectral tau and collocation methods for solving linear and nonlinear multiterm fractional differential equations (FDEs) on the half line. A new formula expressing the Caputo fractional derivatives of modified generalized Laguerre polynomials of any degree and for any fractional order in terms of the modified generalized Laguerre polynomials themselves is derived. An efficient direct solver technique is proposed for solving the linear multiterm FDEs with constant coefficients on the half line using a modified generalized Laguerre tau method. The spatial approximation with its Caputo fractional derivatives is based on modified generalized Laguerre polynomials L-i((alpha,beta)) (x) with x is an element of Lambda = (0, infinity), alpha > -1, and beta > 0, and i is the polynomial degree. We implement and develop the modified generalized Laguerre collocation method based on the modified generalized Laguerre-Gauss points which is used as collocation nodes for solving nonlinear multiterm FDEs on the half line.Article Optimal Control for a Variable-Order Diffusion-Wave Equation With a Reaction Term; a Numerical Study(Elsevier B.V., 2024) Megahed, F.; Shatta, S.A.; Baleanu, D.; Sweilam, N.H.In this paper, optimal control for a variable-order diffusion-wave equation with a reaction term is numerically studied, where the variable-order operator is defined in the sense of Caputo proportional constant. Necessary optimality conditions for the control problem are derived. Existence and uniqueness for the solutions of fractional optimal control problem are derived. The nonstandard weighted average finite difference method and the nonstandard leap-frog method are developed to study numerically the proposed problem. Moreover, the stability analysis of the methods is proved. Finally, in order to characterise the memory property of the proposed model, three test examples are given. It is found that the nonstandard weighted average finite difference method can be applied to study such variable-order fractional optimal control problems simply and effectively. © 2024 The Author(s)Article Citation - Scopus: 7Heuristic Computing With Active Set Method for the Nonlinear Rabinovich–fabrikant Model(Elsevier Ltd, 2023) Baleanu, D.; E Alhazmi, S.; Ben Said, S.; Sabir, Z.The current study shows a reliable stochastic computing heuristic approach for solving the nonlinear Rabinovich-Fabrikant model. This nonlinear model contains three ordinary differential equations. The process of stochastic computing artificial neural networks (ANNs) has been applied along with the competences of global heuristic genetic algorithm (GA) and local search active set (AS) methodologies, i.e., ANNs-GAAS. The construction of merit function is performed through the differential Rabinovich-Fabrikant model. The results obtained through this scheme are simple, reliable, and accurate, which have been calculated to optimize the merit function by using the GAAS method. The comparison of the obtained results through this scheme and the conventional reference solutions strengthens the correctness of the proposed method. Ten numbers of neurons along with the log-sigmoid transfer function in the neural network structure have been used to solve the model. The values of the absolute error are performed around 10−07 and 10−08 for each class of the Rabinovich-Fabrikant model. Moreover, the reliability of the ANNs-GAAS approach is observed by using different statistical approaches for solving the Rabinovich-Fabrikant model. © 2023 The Authors