Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 8Citation - Scopus: 35A Modified Generalized Laguerre Spectral Method for Fractional Differential Equations on the Half Line(Hindawi Ltd, 2013) Baleanu, D.; Bhrawy, A. H.; Taha, T. M.This paper deals with modified generalized Laguerre spectral tau and collocation methods for solving linear and nonlinear multiterm fractional differential equations (FDEs) on the half line. A new formula expressing the Caputo fractional derivatives of modified generalized Laguerre polynomials of any degree and for any fractional order in terms of the modified generalized Laguerre polynomials themselves is derived. An efficient direct solver technique is proposed for solving the linear multiterm FDEs with constant coefficients on the half line using a modified generalized Laguerre tau method. The spatial approximation with its Caputo fractional derivatives is based on modified generalized Laguerre polynomials L-i((alpha,beta)) (x) with x is an element of Lambda = (0, infinity), alpha > -1, and beta > 0, and i is the polynomial degree. We implement and develop the modified generalized Laguerre collocation method based on the modified generalized Laguerre-Gauss points which is used as collocation nodes for solving nonlinear multiterm FDEs on the half line.Article Citation - WoS: 35Citation - Scopus: 74Research Article on Fractional Sirc Model With Salmonella Bacterial Infection(Hindawi Ltd, 2014) Baleanu, Dumitru; Lakshmanan, S.; Rakkiyappan, R.; Rihan, Fathalla A.We propose a fractional order SIRC epidemic model to describe the dynamics of Salmonella bacterial infection in animal herds. The infection-free and endemic steady sates, of such model, are asymptotically stable under some conditions. The basic reproduction number R-0 is calculated, using next-generation matrix method, in terms of contact rate, recovery rate, and other parameters in the model. The numerical simulations of the fractional order SIRC model are performed by Caputo's derivative and using unconditionally stable implicit scheme. The obtained results give insight to the modelers and infectious disease specialists.Article Citation - Scopus: 2A Paradox of the Average Waiting Time for the Case of a Single Bottleneck on the Commuters' Route(Hindawi Ltd, 2021) Kirkavak, Nureddin; Alpay, Ayse Nilay; Ozaktas, HakanAverage waiting time is considered as one of the basic performance indicators for a bottleneck zone on a route for commuter traffic. It turns out that the average waiting time in a queue remains paradoxically unchanged regardless of how fast the queue dissolves for a single bottleneck problem. In this study, the paradox is verified theoretically for the deterministic case with constant arrival and departure rates. Consistent results with the deterministic case have also been obtained by simulation runs for which vehicle interarrival time is a random variable. Results are tabulated for interarrival times which have uniform, triangular, normal, and exponential distributions along with a statistical verification of the average waiting time paradox.Article A k-Dimensional System of Fractional Finite Difference Equations(Hindawi Ltd, 2014) Baleanu, Dumitru; Rezapour, Shahram; Salehi, SaeidWe investigate the existence of solutions for a k-dimensional system of fractional finite difference equations by using the Kranoselskii's fixed point theorem. We present an example in order to illustrate our results.Article Citation - WoS: 32Citation - Scopus: 42Numerical Solution of a Kind of Fractional Parabolic Equations Via Two Difference Schemes(Hindawi Ltd, 2013) Baleanu, Dumitru; Atangana, AbdonA kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this time-fractional parabolic equation with two difference schemes. The explicit and the implicit schemes in this case are stable under some conditions.Article Citation - WoS: 4Citation - Scopus: 5Numerical Solution of a Class of Functional-Differential Equations Using Jacobi Pseudospectral Method(Hindawi Ltd, 2013) Alghamdi, M. A.; Baleanu, D.; Bhrawy, A. H.The shifted Jacobi-Gauss-Lobatto pseudospectral (SJGLP) method is applied to neutral functional-differential equations (NFDEs) with proportional delays. The proposed approximation is based on shifted Jacobi collocation approximation with the nodes of Gauss-Lobatto quadrature. The shifted Legendre-Gauss-Lobatto Pseudo-spectral and Chebyshev-Gauss-Lobatto Pseudo-spectral methods can be obtained as special cases of the underlying method. Moreover, the SJGLP method is extended to numerically approximate the nonlinear high-order NFDE with proportional delay. Some examples are displayed for implicit and explicit forms of NFDEs to demonstrate the computation accuracy of the proposed method. We also compare the performance of the method with variational iteration method, one-leg theta-method, continuous Runge-Kutta method, and reproducing kernel Hilbert space method.Article Citation - WoS: 5Citation - Scopus: 14Mappings for Special Functions on Cantor Sets and Special Integral Transforms Via Local Fractional Operators(Hindawi Ltd, 2013) Baleanu, Dumitru; Baleanu, Mihaela Cristina; Cheng, De-Fu; Yang, Xiao-Jun; Zhao, YangThe mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.Article Citation - WoS: 10Citation - Scopus: 8Lower and Upper Solutions Method for Positive Solutions of Fractional Boundary Value Problems(Hindawi Ltd, 2013) Mohammadzadeh, B.; Neamaty, A.; Baleanu, D.; Darzi, R.; Bleanu, D.We apply the lower and upper solutions method and fixed-point theorems to prove the existence of positive solution to fractional boundary value problem D(0+)(alpha)u(t) + f(t, u(t)) = 0, 0 < t < 1, 2 < alpha <= 3, u(0) = u'(0) = 0, D-0(alpha-1),u(1) = beta u(xi), 0 < xi < 1, where D-0+(alpha) denotes Riemann-Liouville fractional derivative, beta is positive real number, beta xi(alpha-1) >= 2 Gamma(alpha), and f is continuous on [0, 1] x [0,infinity). As an application, one example is given to illustrate the main result.Article Citation - WoS: 43Citation - Scopus: 80Local Fractional Sumudu Transform With Application To Ivps on Cantor Sets(Hindawi Ltd, 2014) Golmankhaneh, Alireza Khalili; Baleanu, Dumitru; Yang, Xiao-Jun; Srivastava, H. M.Local fractional derivatives were investigated intensively during the last few years. The coupling method of Sumudu transform and local fractional calculus (called as the local fractional Sumudu transform) was suggested in this paper. The presented method is applied to find the non differentiable analytical solutions for initial value problems with local fractional derivative. The obtained results are given to show the advantages.Article Citation - WoS: 7Citation - Scopus: 15Hybrid Bernstein Block-Pulse Functions Method for Second Kind Integral Equations With Convergence Analysis(Hindawi Ltd, 2014) Baleanu, Dumitru; Babaei, Fereshteh; Alipour, MohsenWe introduce a new combination of Bernstein polynomials (BPs) and Block-Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block-Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.