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: 16Citation - Scopus: 22Some Fixed Point Results for Tac-Type Contractive Mappings(Hindawi Ltd, 2016) Tas, Kenan; Ansari, Arslan Hojat; Chandok, SumitWe prove some fixed point results for new type of contractive mappings using the notion of cyclic admissible mappings in the framework of metric spaces. Our results extend, generalize, and improve some well-known results from literature. Some examples are given to support our main results.Editorial Citation - WoS: 2Recent Development in Partial Differential Equations and Their Applications(Hindawi Ltd, 2014) Khalique, Chaudry M.; Baleanu, Dumitru; Jafari, HosseinArticle 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 - WoS: 103Citation - Scopus: 114On Coupled Systems of Time-Fractional Differential Problems by Using a New Fractional Derivative(Hindawi Ltd, 2016) Baleanu, Dumitru; Etemad, Sina; Rezapour, Shahram; Alsaedi, AhmedThe existence of solutions for a coupled system of time-fractional differential equations including continuous functions and the Caputo-Fabrizio fractional derivative is examined. After that we investigated a coupled system of time-fractional differential inclusions including compact-and convex-valued L-1-Caratheodory multifunctions and the Caputo-Fabrizio fractional derivative.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: 5Citation - Scopus: 5Bessel Beam Diffraction by an Aperture in an Opaque Screen(Hindawi Ltd, 2015) Basdemir, Husnu DenizThe scattering of the Bessel beam by a circular aperture in an opaque screen is investigated by the geometrical theory of diffraction approach. The geometrical optics and diffracted and scattered fields are obtained. The effect of the aperture to the scattering process is analyzed. The uniform versions of field expressions are derived. The geometrical optics and diffracted and scattered fields are examined numerically.Article Citation - WoS: 6Citation - Scopus: 7Raman Spectra of Nanodiamonds: New Treatment Procedure Directed for Improved Raman Signal Marker Detection(Hindawi Ltd, 2013) Baleanu, Dumitru; Povarova, Diana; Salah, Numan; Habib, Sami S.; Memic, Adnan; Nigmatullin, Raoul R.Detonation nanodiamonds (NDs) have shown to be promising agents in several industries, ranging from electronic to biomedical applications. These NDs are characterized by small particle size ranging from 3 to 6 nm, while having a reactive surface and a stable inert core. Nanodiamonds can exhibit novel intrinsic properties such as fluorescence, high refractive index, and unique Raman signal making them very attractive imaging agents. In this work, we used several nanodiamond preparations for Raman spectroscopic studies. We exposed these nanodiamonds to increasing temperature treatments at constant heating rates (425-575 degrees C) aiding graphite release. We wanted to correlate changes in the nanodiamond surface and properties with Raman signal which could be used as a detection marker. These observations would hold potential utility in biomedical imaging applications. First, the procedure of optimal linear smoothing was applied successfully to eliminate the high-frequency fluctuations and to extract the smoothed Raman spectra. After that we applied the secondary Fourier transform as the fitting function based on some significant set of frequencies. The remnant noise was described in terms of the beta-distribution function. We expect this data treatment to provide better results in biomolecule tracking using nanodiamond base Raman labeling.Article Citation - WoS: 2Citation - Scopus: 2On Classification of Pdz Domains: a Computational Study(Hindawi Ltd, 2013) Memic, Adnan; Baleanu, Dumitru; Aftab, WasimOur goal in this present study is to introduce new wavelet based methods for differentiating and classifying Class I and Class II PDZ domains and compare the resulting signals. PDZ domains represent one of the most common protein homology regions playing key roles in several diseases. To perform the classification, we developed two methods. The first of our methods was comparable to the standard wavelet approaches while the second one surpasses it in recognition accuracy. Our models exhibited interesting results, and we anticipate that it can be used as a computational technique to screen out the misfit candidates and to reduce the search space, while achieving high classification and accuracy.Article Citation - WoS: 9Citation - Scopus: 22Local Fractional Discrete Wavelet Transform for Solving Signals on Cantor Sets(Hindawi Ltd, 2013) Baleanu, Dumitru; Cattani, Carlo; Cheng, De-Fu; Yang, Xiao-Jun; Zhao, YangThe discrete wavelet transform via local fractional operators is structured and applied to process the signals on Cantor sets. An illustrative example of the local fractional discrete wavelet transform is given.