WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
Browse
39 results
Search Results
Article Citation - WoS: 5Citation - Scopus: 5Performance Evaluation of Matched Asymptotic Expansions for Fractional Differential Equations With Multi-Order(Soc Matematice Romania, 2016) Baleanu, Dumitru; Baleanu, Dumitru; Sayevand, Khosro; MatematikAn extension of the concept of the asymptotic expansions method is presented in this paper. The multi-order differential equations of fractional order are investigated and the convergence of the proposed method is proven. The reported results show that the present approach is very effective and accurate and also are in good agreement with the ones in the literature.Article Citation - WoS: 34Citation - Scopus: 30New Solutions of the Transport Equations in Porous Media Within Local Fractional Derivative(Editura Acad Romane, 2016) Zhang, Yu; Baleanu, Dumitru; Baleanu, Dumitru; Yang, Xiao-Jun; MatematikIn this manuscript we use the series expansion method within local fractional derivative to obtain the solutions of both homogeneous and non-homogeneous transport equations. The new reported solutions are able to describe more efficiently the behavior of solutions of the transport phenomena in porous media.Article Citation - WoS: 9Analytic Study of Allen-Cahn Equation of Fractional Order(int Center Scientific Research & Studies, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; MatematikThe key purpose of the present article is to analyze the Allen Cahn equation of fractional order. The fractional Allen-Cahn equation models the process of phase separation in iron alloys, along with order-disorder transitions. The analytical technique is employed to investigate the fractional model of Allen-Cahn equation. The numerical results are shown graphically. The outcomes show that the analytical technique is very efficient and user friendly for handling nonlinear fractional differential equations describing the real world problems.Article Citation - WoS: 16Citation - Scopus: 17Fractional Synchronization of Chaotic Systems With Different Orders(Editura Acad Romane, 2012) Razminia, Abolhassan; Baleanu, Dumitru; Baleanu, Dumitru; MatematikIn this paper, we consider two chaotic systems with different orders. First, we consider the case when one of them is fractional order (master system) and another one is integer order (slave system). Second, we consider the case when both of them are fractional order but the orders are different. Using a fractional synchronization scheme in the presence of discrepancy between initial conditions of these systems for both cases the trajectories of the slave system are forced to track the master system trajectories. The effectiveness of the proposed technique is verified by numerical simulations for Chen systems.Article Citation - WoS: 31Citation - Scopus: 34Transport Equations in Fractal Porous Media Within Fractional Complex Transform Method(Editura Acad Romane, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; He, Ji-Huan; MatematikIn this paper we investigate the transport equations in fractal porous media by using the fractional complex transform method. The local fractional linear and nonlinear transport equations with local fractional time and space fractional derivatives are obtained. The proposed models adequately describe the fractal transport processes.Article Citation - WoS: 59Citation - Scopus: 66New Aspects of the Motion of a Particle in a Circular Cavity(Editura Acad Romane, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; MatematikIn this work, we consider the free motion of a particle in a circular cavity. For this model, we obtain the classical and fractional Lagrangian as well as the fractional Hamilton's equations (FHEs) of motion. The fractional equations are formulated in the sense of Caputo and a new fractional derivative with Mittag-Leffler nonsingular kernel. Numerical simulations of the FHEs within these two fractional operators are presented and discussed for some fractional derivative orders. Numerical results are based on a discretization scheme using the Euler convolution quadrature rule for the discretization of the convolution integral. Simulation results show that the fractional calculus provides more flexible models demonstrating new aspects of the real-world phenomena.Article Citation - WoS: 66Citation - Scopus: 63An Accurate Numerical Technique for Solving Fractional Optimal Control Problems(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; MatematikIn this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives are used together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem. For confirming the efficiency and accuracy of the proposed technique, an illustrative numerical example is introduced with its approximate solution.Article Citation - WoS: 38Citation - Scopus: 39On the Mittag-Leffler Stability of Q-Fractional Nonlinear Dynamical Systems(Editura Acad Romane, 2011) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Abdeljawad, Thabet; Gundogdu, Emrah; Baleanu, Dumitru; Baleanu, Dumitru; MatematikIn this article, analogous to the definition of the exponential stability of ordinary dynamical systems and the Mittag-Leffler stability of the fractional dynamical systems, we consider the Mittag-Leffler stability for q-fractional nonlinear dynamical systems. The sufficient conditions for Mittag-Leffler stability of such dynamical systems within the framework of the q-fractional Caputo derivative are studied.Article Citation - WoS: 65Citation - Scopus: 65Solutions of the Telegraph Equations Using a Fractional Calculus Approach(Editura Acad Romane, 2014) Gomez Aguilar, Jose Francisco; Baleanu, Dumitru; Baleanu, Dumitru; MatematikIn this paper, the fractional differential equation for the transmission line without losses in terms of the fractional time derivatives of the Caputo type is considered. In order to keep the physical meaning of the governing parameters, new parameters a and a were introduced. These parameters characterize the existence of the fractional components in the system. A relation between these parameters is also reported. Fractional differential equations are examined with both temporal and spatial fractional derivatives. We show a few illustrative examples when the wave periodicity is broken in either temporal or spatial variables. Finally, we present the output of numerical simulations that were performed with both temporal and spatial fractional derivatives.Article Citation - WoS: 9Citation - Scopus: 10A Perturbative Analysis of Nonlinear Cubic-Quintic Duffing Oscillators(Editura Acad Romane, 2014) Sayevand, Khosro; Baleanu, Dumitru; Baleanu, Dumitru; Fardi, Mojtaba; MatematikDuffing oscillators comprise one of the canonical examples of Hamilton systems. The presence of a quintic term makes the cubic-quintic Duffing oscillator more complex and interesting to study. In this paper, the homotopy analysis method (HAM) is used to obtain the analytical solution for the nonlinear cubic-quintic Duffing oscillators. The HAM helps to obtain the frequency omega in the form of approximation series of a convergence control parameter (h) over bar. The valid region of (h) over bar is determined by plotting the omega - (h) over bar curve and afterwards we compared the obtained results with the exact solutions.