Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 15Citation - Scopus: 23Optical Solitons With Nonlinear Dispersion in Parabolic Law Medium and Three-Component Coupled Nonlinear Schrodinger Equation(Springer, 2022) Sulaiman, Tukur Abdulkadir; Alshomrani, Ali S.; Baleanu, Dumitru; Yusuf, AbdullahiThe current study looks at two different nonlinear Schrodinger equations. These equations have several applications in science and engineering, such as nonlinear fiber optics, electromagnetic field waves, and signal processing via optical fibers. In this study, we investigate these equations using an efficient integration strategy known as complex envelop antazs. As a result, we obtain novel solutions such as bright, dark, and combined dark-bright soliton solutions. Important physical aspects have been depicted in three dimensions and contour plots for clear interpretation of the acquired solutions.Article Citation - WoS: 91Citation - Scopus: 98Novel Hyperbolic and Exponential Ansatz Methods To the Fractional Fifth-Order Korteweg-De Vries Equations(Springer, 2020) Nuruddeen, R., I; Ali, Khalid K.; Muhammad, Lawal; Osman, M. S.; Baleanu, Dumitru; Park, ChoonkilThis paper aims to investigate the class of fifth-order Korteweg-de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.Article Citation - WoS: 38Citation - Scopus: 63A Fractional Derivative With Two Singular Kernels and Application To a Heat Conduction Problem(Springer, 2020) Jleli, Mohamed; Kumar, Sunil; Samet, Bessem; Baleanu, DumitruIn this article, we suggest a new notion of fractional derivative involving two singular kernels. Some properties related to this new operator are established and some examples are provided. We also present some applications to fractional differential equations and propose a numerical algorithm based on a Picard iteration for approximating the solutions. Finally, an application to a heat conduction problem is given.Article Citation - WoS: 25Citation - Scopus: 32Ternary-Fractional Differential Transform Schema: Theory and Application(Springer, 2019) Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; Yousef, FerasIn this article, we propose a novel fractional generalization of the three-dimensional differential transform method, namely the ternary-fractional differential transform method, that extends its applicability to encompass initial value problems in the fractal 3D space. Several illustrative applications, including the Schrodinger, wave, Klein-Gordon, telegraph, and Burgers' models that are fully embedded in the fractal 3D space, are considered to demonstrate the superiority of the proposed method compared with other generalized methods in the literature. The obtained solution is expressed in a form of an (alpha) over bar -fractional power series, with easily computed coefficients, that converges rapidly to its closed-form solution. Moreover, the projection of the solutions into the integer 3D space corresponds with the solutions of the classical copies for these models. This reveals that the suggested technique is effective and accurate for handling many other linear and nonlinear models in the fractal 3D space. Thus, research on this trend is worth tracking.Article Citation - WoS: 41Citation - Scopus: 44Fractional Euler-Lagrange Equations Revisited(Springer, 2012) Baleanu, Dumitru; Herzallah, Mohamed A. E.This paper presents the necessary and sufficient optimality conditions for the Euler-Lagrange fractional equations of fractional variational problems with determining in which spaces the functional must exist where the functional contains right and left fractional derivatives in the Riemann-Liouville sense and the upper bound of integration less than the upper bound of the interval of the fractional derivative. In order to illustrate our results, one example is presented.Article Citation - WoS: 48Citation - Scopus: 57Fractional Variational Optimal Control Problems With Delayed Arguments(Springer, 2010) Jarad, Fahd; Abdeljawad, Thabet; Baleanu, DumitruThe paper deals with optimal control problems in the presence of delay in the state variables as well as the presence of the Riemann-Liouville fractional derivatives of the state variables. One example is analyzed in detail.Article Citation - WoS: 70Citation - Scopus: 80Fractional-Order Euler-Lagrange Equations and Formulation of Hamiltonian Equations(Springer, 2009) Baleanu, Dumitru; Herzallah, Mohamed A. E.This paper presents the fractional order Euler-Lagrange equations and the transversality conditions for fractional variational problems with fractional integral and fractional derivatives defined in the sense of Caputo and Riemann-Liouville. A fractional Hamiltonian formulation was developed and some illustrative examples were treated in detail.Article Citation - WoS: 18Citation - Scopus: 26Fractional Wkb Approximation(Springer, 2009) Altarazi, Ibrahim M. A.; Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab M.Wentzel-Kramer-Brillouin (WKB) approximation for fractional systems is investigated in this paper using the fractional calculus. In the fractional case, the wave function is constructed such that the phase factor is the same as the Hamilton's principle function S. To demonstrate our proposed approach, two examples are investigated in detail.