WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Explicit Commutativity and Stability Theories for Second-Order Heun's LTVSs(World Scientific Publ Co Pte Ltd, 2025) Ibrahim, Salisu; Baleanu, DumitruThis paper derived and proved the simplex explicit commutativity theories and conditions for second-order linear time-varying systems (LTVSs) with both zero and nonzero initial conditions (ICs). We consider Heun's LTVS as a case study to verify the explicit commutative results, which were supported by simulation. Furthermore, we investigate the sensitivity of Heun's LTVS, the robustness of Heun's LTVS, the stability of Heun's LTVS, the effects due to disturbance on Heun's LTVS and the problem associated with commutativity of Heun's LTVS. These findings will tackle many problems related to the commutativity theory, the stability of LTVS, design and behavior of control systems, which have made an essential contribution and play a vital role in science and engineering. By considering a sinusoid of amplitude 5, bias -3 and frequency 7, with parameters c2,c1,c0 and an arbitrary choosing initial time (IT) t0 to be and also the initial states yA(0),yB(0),yA '(0),yB '(0), several quantitative results obtained by simulation show that the Heun's LTVSs AB and BA give the same output response, AB and BA are commutative under certain conditions and proved to be unstable numerically. Moreover, the quantitative results proved that the Heun's LTVSs AB and BA are very sensitive toward changes in ICs and parameters. Disturbance between the connections also affects the systems AB and BA, these give different responses as a result of tampering with the conditions, hence commutativity is not satisfied. Several examples have been given to support our fact explicitly and numerically. However, the explicit commutativity and stability for Heun's LTVS have not been in the literature yet, and this paper presents it for the first time. The results are well verified by simulation and treated with Wolfram Mathematica 11.Article Citation - WoS: 36Citation - Scopus: 41Numerical Treatment of Coupled Nonlinear Hyperbolic Klein-Gordon Equations(Editura Acad Romane, 2014) Doha, E. H.; Baleanu, Dumitru; Bhrawy, A. H.; Baleanu, D.; Abdelkawy, M. A.; MatematikA semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GL-C) method is proposed and developed for the numerical solution of the spatial variable for two nonlinear coupled Klein-Gordon (KG) partial differential equations. The general Jacobi-Gauss-Lobatto points are used as collocation nodes in this approach. The main characteristic behind the J-GL-C approach is that it reduces such problems to solve a system of ordinary differential equations (SODEs) in time. This system is solved by diagonally-implicit Runge-Kutta-Nystrom scheme. Numerical results show that the proposed algorithm is efficient, accurate, and compare favorably with the analytical solutions.Article Citation - WoS: 4Citation - Scopus: 4Fractional Vector Calculus in the Frame of a Generalized Caputo Fractional Derivative(Univ Politehnica Bucharest, Sci Bull, 2018) Jarad, Fahd; Gambo, Yusuf Ya'u; Baleanu, Dumitru; Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet; Abdeljawad, Thabet; MatematikThe authors in [1] recently introduced a new generalized fractional derivative on AC(y)(n)[a ,b] and C-y(n)[a, b], and defined their Caputo version. This derivative contains two parameters and reduces to the classical Caputo derivatives if one of these parameters tend to certain values. From here and after, by generalized Caputo fractional derivative, we refer to the Caputo version of the generalized fractional derivative. This paper studies the generalized Caputo fractional derivative and establishes the Fundamental Theorem of Fractional Calculus (FTFC) in the sense of this derivative. The fundamental results are used in establishing some vital theorems and then applied to vector calculus.Editorial From the Guest Editors Contemporary Modelling Methods in Heat, Mass, and Fluid Flow Special Collection of Articles(Vinca inst Nuclear Sci, 2017) Hristov, Jordan; Baleanu, Dumitru; Baleanu, Dumitru; Atangana, Abdon; MatematikArticle Citation - WoS: 16Citation - Scopus: 16Comparative Application of Wavelet Approaches To Absorption and Ratio Spectra for the Simultaneous Determination of Diminazene Aceturate and Phenazone in Veterinary Granules for Injection(Govi-verlag Pharmazeutischer verlag Gmbh, 2005) Dinç, E; Baleanu, Dumitru; Kanbur, M; Baleanu, D; MatematikA comparison of two wavelet approaches, Daubechies and reverse Biorthogonal, is described for the quantitative resolution of a binary mixture of diminazene aceturate (DIMA) and phenazone (PHE) in veterinary granules for injection without any chemical separation. These two approaches were specified as db4 (a = 180) and rbior3.7 (a = 125) respectively, after testing the signal analysis parameters for the overlapping absorption spectra and ratio spectra. In the first step db4 (a = 180) was applied to the original absorbance data vector of DIMA and PHE. In the second step rbio3.7 (a = 125) was applied to the ratio spectra data vectors of DIMA using the divisor PHE. The same approach was also subjected to the ratio spectra of PHE using the divisor DIMA. The db4 (a = 180) and rbior3.7 (a = 125) calibration graphs were constructed using the transformation values obtained in the wavelet domain. In the method validation, the wavelet calibration functions were tested using synthetic mixtures and the standard addition technique. The simultaneous quantitative analysis of DIMA and PHE in the commercial veterinary preparation was achieved by the elaborated methods. The assay results were compared with each other and good agreement was observed.Article Citation - WoS: 60Citation - Scopus: 68Lyapunov-Krasovskii Stability Theorem for Fractional Systems With Delay(Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, D.; Ranjbar N, A.; Abdeljawad, Thabet; Sadati R, S. J.; Delavari, R. H.; Abdeljawad (Maraaba), T.; Gejji, V.; MatematikFractional calculus techniques and methods started to be applied during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative and we extended Lyapunov-Krasovskii theorem for the fractional nonlinear systems.Article Citation - WoS: 19Citation - Scopus: 18On Fractional Coupled Whitham-Broer Equations(Editura Acad Romane, 2011) Kadem, Abdelouahab; Baleanu, Dumitru; Baleanu, Dumitru; MatematikFinding the fractional version of a given classical nonlinear equation or to a given system of differential equations is still an open problem in the field of the fractional calculus. In this paper the homotopy perturbation method is used to find an analytical approximate solution for the coupled Whitham-Broer-Kaup equations. The obtained results indicate that the method is efficient and accurate.Article Citation - WoS: 34Citation - Scopus: 38On the Fractional-Order Diffusion-Wave Process(Editura Acad Romane, 2010) Herzallah, Mohamed A. E.; Baleanu, Dumitru; El-Sayed, Ahmed M. A.; Baleanu, Dumtru; MatematikOne of the main applications of the fractional calculus, integration and differentiation of arbitrary orders is the modelling of the intermediate physical processes. Here we formulate a more general model which represents the diffusion wave process in all its cases, and give some examples discussing these different cases.Article Citation - WoS: 19Citation - Scopus: 18New Results for Multidimensional Diffusion Equations in Fractal Dimensional Space(Editura Acad Romane, 2016) Ma, Min; Baleanu, Dumitru; Baleanu, Dumitru; Gasimov, Yusif S.; Yang, Xiao-Jun; MatematikThe multidimensional diffusion equations in fractal dimensional space started to play an important role in physics. In this paper we present the analytical solutions of the multidimensional diffusion equations in fractal dimensional spaces by using the method of separation of variables. The graphs of the exact solutions are presented and the accuracy and efficiency of the approach are revealed for a class of local fractional partial differential equations.Article Citation - WoS: 28Citation - Scopus: 33Lagrangian Formulation of Maxwell's Field in Fractional D Dimensional Space-Time(Editura Acad Romane, 2010) Muslih, Sami I.; Baleanu, Dumitru; Saddallah, Madhat; Baleanu, Dumitru; Rabei, Eqab; MatematikThe Lagrangian formulation for field systems is obtained in fractional space-time fractional dimensions D = D-space + D-time. The equations of motion for Maxwell's field are obtained. It is shown that the form of Maxwell's equations in fractional dimensional space are not invariant and they can be solved in the same manner as in the integer space-time dimensions.