WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 4Citation - Scopus: 4Variational Iteration Method - a Promising Technique for Constructing Equivalent Integral Equations of Fractional Order(Sciendo, 2013) Wu, Guo-Cheng; Baleanu, Dumitru; Wang, Yi-HongThe variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method's new role.Article Citation - WoS: 137Citation - Scopus: 151Variational Iteration Method for the Burgers' Flow With Fractional Derivatives-New Lagrange Multipliers(Elsevier Science inc, 2013) Baleanu, Dumitru; Wu, Guo-ChengThe flow through porous media can be better described by fractional models than the classical ones since they include inherently memory effects caused by obstacles in the structures. The variational iteration method was extended to find approximate solutions of fractional differential equations with the Caputo derivatives, but the Lagrange multipliers of the method were not identified explicitly. In this paper, the Lagrange multiplier is determined in a more accurate way and some new variational iteration formulae are presented. (C) 2013 Elsevier Inc. All rights reserved.Article Citation - WoS: 69Citation - Scopus: 103Variational Iteration Method for Fractional Calculus - a Universal Approach by Laplace Transform(Springeropen, 2013) Baleanu, Dumitru; Wu, Guo-ChengA novel modification of the variational iteration method (VIM) is proposed by means of the Laplace transform. Then the method is successfully extended to fractional differential equations. Several linear fractional differential equations are analytically solved as examples and the methodology is demonstrated.Article Citation - WoS: 31Citation - Scopus: 36Mittag-Leffler Function for Discrete Fractional Modelling(Elsevier, 2016) Baleanu, Dumitru; Zeng, Sheng-Da; Luo, Wei-Hua; Wu, Guo-ChengFrom the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta's sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function. (C) 2015 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University.Article Citation - WoS: 69Citation - Scopus: 68New Applications of the Variational Iteration Method - From Differential Equations To Q-Fractional Difference Equations(Springeropen, 2013) Baleanu, Dumitru; Wu, Guo-ChengThe non-classical calculi such as q-calculus, fractional calculus and q-fractional calculus have been hot topics in both applied and pure sciences. Then some new linear and nonlinear models have appeared. This study mainly concentrates on the analytical aspects, and the variational iteration method is extended in a new way to solve an initial value problem.Article Citation - WoS: 64Citation - Scopus: 67Novel Mittag-Leffler Stability of Linear Fractional Delay Difference Equations With Impulse(Pergamon-elsevier Science Ltd, 2018) Baleanu, Dumitru; Huang, Lan-Lan; Wu, Guo-ChengIn this letter we propose a class of linear fractional difference equations with discrete time delay and impulse effects. The exact solutions are obtained by use of a discrete Mittag-Leffler function with delay and impulse. Besides, we provide comparison principle, stability results and numerical illustration. (C) 2018 Elsevier Ltd. All rights reserved.Conference Object Citation - WoS: 112Citation - Scopus: 120Fractional Impulsive Differential Equations: Exact Solutions, Integral Equations and Short Memory Case(Walter de Gruyter Gmbh, 2019) Zeng, De-Qiang; Baleanu, Dumitru; Wu, Guo-ChengFractional impulsive differential equations are revisited first. Some fundamental solutions of linear cases are given in this study. One straightforward technique without using integral equation is adopted to obtain exact solutions which are given by use of piecewise functions. Furthermore, a class of short memory fractional differential equations is proposed and the variable case is discussed. Mittag-Leffler solutions with impulses are derived which both satisfy the equations and impulsive conditions, respectively.Article Citation - WoS: 102Citation - Scopus: 111Mittag-Leffler Stability Analysis of Fractional Discrete-Time Neural Networks Via Fixed Point Technique(inst Mathematics & informatics, 2019) Liu, Jinliang; Baleanu, Dumitru; Wu, Kai-Teng; Wu, Guo-Cheng; Abdeljawad, ThabetA class of semilinear fractional difference equations is introduced in this paper. The fixed point theorem is adopted to find stability conditions for fractional difference equations. The complete solution space is constructed and the contraction mapping is established by use of new equivalent sum equations in form of a discrete Mittag-Leffler function of two parameters. As one of the application, finite-time stability is discussed and compared. Attractivity of fractional difference equations is proved, and Mittag-Leffler stability conditions are provided. Finally, the stability results are applied to fractional discrete-time neural networks with and without delay, which show the fixed point technique's efficiency and convenience.Article Citation - WoS: 12Citation - Scopus: 12Analysis of Fractional Non-Linear Diffusion Behaviors Based on Adomian Polynomials(Vinca inst Nuclear Sci, 2017) Baleanu, Dumitru; Luo, Wei-Hua; Wu, Guo-ChengA time-fractional non-linear diffusion equation of two orders is considered to investigate strong non-linearity through porous media. An equivalent integral equation is established and Adomian polynomials are adopted to linearize non-linear terms. With the Taylor expansion of fractional order, recurrence formulae are proposed and novel numerical solutions are obtained to depict the diffusion behaviors more accurately. The result shows that the method is suitable for numerical simulation of the fractional diffusion equations of multi-orders.