Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 16Citation - Scopus: 15On Numerical Solution of the Time Fractional Advection-Diffusion Equation Involving Atangana-Baleanu Derivative(Sciendo, 2019) Inc, Mustafa; Bayram, Mustafa; Baleanu, Dumitru; Partohaghighi, MohammadA powerful algorithm is proposed to get the solutions of the time fractional Advection-Diffusion equation(TFADE): (ABC)D(0+)(,t)(beta)u(x, t) = zeta u(xx)(x, t) - kappa u(x)(x, t) + F(x, t), 0 < beta <= 1. The time-fractional derivative (ABC)D(0+)(,t)(beta)u(x, t) is described in the Atangana-Baleanu Caputo concept. The basis of our approach is transforming the original equation into a new equation by imposing a transformation involving a fictitious coordinate. Then, a geometric scheme namely the group preserving scheme (GPS) is implemented to solve the new equation by taking an initial guess. Moreover, in order to present the power of the presented approach some examples are solved, successfully.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: 2Citation - Scopus: 2Fractional Order Modelling of Zero Length Column Desorption Response for Adsorbents With Variable Particle Sizes(Sciendo, 2013) Zaman, Sharif F.; Baleanu, Dumitru; Tenreiro Machado, J. A.; Machado, J.A.TenreiroThis manuscript analyses the data generated by a Zero Length Column (ZLC) diffusion experimental set-up, for 1,3 Di-isopropyl benzene in a 100% alumina matrix with variable particle size. The time evolution of the phenomena resembles those of fractional order systems, namely those with a fast initial transient followed by long and slow tails. The experimental measurements are best fitted with the Harris model revealing a power law behavior.Article Citation - WoS: 4Citation - Scopus: 4Cosmological Perturbations in Frw Model With Scalar Field Within Hamilton-Jacobi Formalism and Symplectic Projector Method(Sciendo, 2006) Baleanu, DumitruThe Hamilton-Jacobi analysis is applied to the dynamics of the scalar fluctuations about the Friedmann-Robertson-Walker (FRW) metric. The gauge conditions are determined from the consistency conditions. The physical degrees of freedom of the model are obtained by the symplectic projector method. The role of the linearly dependent Hamiltonians and the gauge variables in the Hamilton-Jacobi formalism is discussed. (c) Versita Warsaw and Springer-Verlag Berlin Heidelberg. All rights reserved.Article Citation - WoS: 19Citation - Scopus: 23Sliding Observer for Synchronization of Fractional Order Chaotic Systems With Mismatched Parameter(Sciendo, 2012) Senejohnny, Danial M.; Baleanu, Dumitru; Delavari, HadiIn this paper, we propose an observer-based fractional order chaotic synchronization scheme. Our method concerns fractional order chaotic systems in Brunovsky canonical form. Using sliding mode theory, we achieve synchronization of fractional order response with fractional order drive system using a classical Lyapunov function, and also by fractional order differentiation and integration, i.e. differintegration formulas, state synchronization proved to be established in a finite time. To demonstrate the efficiency of the proposed scheme, fractional order version of a well-known chaotic system; Arnodo-Coullet system is considered as illustrative examples.Article Citation - WoS: 34Citation - Scopus: 39Lie Symmetry Analysis and Conservation Laws for the Time Fractional Simplified Modified Kawahara Equation(Sciendo, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, DumitruIn this work, Lie symmetry analysis for the time fractional simplified modified Kawahara (SMK) equation with Riemann-Liouville (RL) derivative, is analyzed. We transform the time fractional SMK equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable. In the reduced equation, the derivative is in the Erdelyi-Kober (EK) sense. We solve the reduced fractional ODE using a power series technique. Using Ibragimov's nonlocal conservation method to time fractional partial differential equations, we compute conservation laws (Cls) for the time fractional SMK equation. Some figures of the obtained explicit solution are presented.Article Citation - WoS: 17Citation - Scopus: 16Integral Inequalities Involving Generalized Erdelyi-Kober Fractional Integral Operators(Sciendo, 2016) Purohit, Sunil Dutt; Prajapati, Jyotindra C.; Baleanu, DumitruUsing the generalized Erdelyi-Kober fractional integrals, an attempt is made to establish certain new fractional integral inequalities, related to the weighted version of the Chebyshev functional. The results given earlier by Purohit and Raina (2013) and Dahmani et al. (2011) are special cases of results obtained in present paper.