Fen - Edebiyat Fakültesi

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A common fixed point theorem of a Greguš type on convex cone metric spaces
(2011) Abdeljawad, Thabet; Karapinar, Erdal; 19184; Matematik
The result of Ćirić [1] on a common fixed point theorem of Greguš type on metric spaces is extended to the class of cone metric spaces. Namely, a common fixed point theorem is proved in s-convex cone metric spaces under the normality of the cone and another common fixed point theorem is proved in convex cone metric spaces under the assumption that the cone is strongly minihedral.
A novelweak fuzzy solution for fuzzy linear system
(2016) Baleanu, Dumitru; Ahmadian, Ali; Ismail, Fudziah; Baleanu, Dumitru; 56389; Matematik
This article proposes a novel weak fuzzy solution for the fuzzy linear system. As a matter of fact, we define the right-hand side column of the fuzzy linear system as a piecewise fuzzy function to overcome the related shortcoming, which exists in the previous findings. The strong point of this proposal is that the weak fuzzy solution is always a fuzzy number vector. Two complex and non-complex linear systems under uncertainty are tested to validate the effectiveness and correctness of the presented method.
A pair of Köthe spaces between which all continuous linear operators are bounded
(2004) Abdeljawad, Thabet; Matematik
A Prelımınary Work On Investıgatıng Unıted Natıons’s Egovernment Crıterıa In Mıddle East Countrıes
(2017) Hussein, Mohammed; Pusatlı, O. Tolga; 51704
The benefits of e-government initiatives empowered by the information and communication technologies, are acknowledged widely with assessment criteria published by the United Nations regularly over the last 15 years. One of the reasons that United Nations has taken such assessment into agenda is the apparent advantages of such initiatives over the citizen, society and government. In parallel literature review and current status of Middle East countries, these issues are investigated with examples: Internet users, awareness and training, culture, intention to use e-government applications of the citizens, portal and interoperability. It is noted that assessment of human capital indices for these countries should be read carefully while considering these topics. The findings reveal the impact of human capital index on evaluating egovernment performance; geographical area and population also affect the adoption of e-government. For this, follow-up work is suggested to investigate the level of information and communication technology and computer literacy along with these factors in the region. This research has limitations which include the sources of information, exclusive economic and legal issues and a number of measurement methods.
An Efficient Algorithm for Solving Nonlinear Systems of Partial Differential Equations with Local Fractional Operators
(Univ Punjab, 2019) Baleanu, Dumitru; Cherif, Mountassir Hamdi; Baleanu, Dumitru; Belghaba, Kacem; Al Qurashi, Maysaa Mohamed; 56389; Matematik
The aim of the present study is to extend the local fractional Sumudu decomposition method (LFSDM) to resolve nonlinear systems of partial differential equations with local fractional derivatives. The derivative operators are taken in the local fractional sense. The LFSDM method provides the solution in a rapid convergent series, which may lead the non-differentiable solution in a closed form, this makes them an appropriate method for similar problems. We have provided some examples to confirm their flexibility in solving these types of systems.
Cantor-type spherical-coordinate method for differential equationswithin local fractional derivatives
(De Gruyter Open LTD, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Yang, XJ; 56389; Matematik
In this article, we utilize the Cantor-type spherical coordinate method to investigate a family of local fractional differential operators on Cantor sets. Some examples are discussed to show the capability of this method for the damped wave, Helmholtz and heat conduction equations defined on Cantor sets. We show that it is a powerful tool to convert differential equations on Cantor sets from Cantorian-coordinate systems to Cantor-type spherical-coordinate systems.
Common fixed point theorems in cone Banach spaces
(2011) Abdeljawad, Thabet; Karapınar, Erdal; Taş, Kenan; 4971; Matematik
Recently, E. Karapınar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.
Complex b-spline collocation method for solving weaklysingular volterra integral equations of the second kind
(Univ Miskolc Inst Math, 2015) Baleanu, Dumitru; Ramezani, M.; Johnston, S. J.; Baleanu, Dumitru; 56389; Matematik
In this paper we propose a new collocation type method for solving Volterra integral equations of the second kind with weakly singular kernels. In this method we use the complex B-spline basics in collocation method for solving Volterra integral. We compare the results obtained by this method with exact solution. A few numerical examples are presented to demonstrate the effectiveness of the proposed method.
Do Users Sacrifice Security for Speed and Ease-of-Use on Smartphones?: A Case Study on Attitude
(2020) Koyuncu, Murat; Nakip, Mahir; Nakip, Mahir; 51704; Uluslararası Ticaret ve Finansman
Storing credentials on smartphones to perform online activities increases ease-of-use (EoU) and speed. However, such practices increase security risks, especially if users use a number of applications or store data on their smartphones. Risks become more complicated by keeping smartphones online. This work aims to find potential relationships between security perceptions of smartphone users and their ease-of-use and speed preferences. Two user attitudes are defined as “not considering risk” and “risk exaggeration.” User ease-of-use and speed preferences are limited with the factors related to storing credentials on a smartphone and always keeping the device online. A survey of 154 participants was conducted through convenience sampling. Through regression analyses, logarithmic causality relations are found between EoU and speed and attitudes of not considering risk or risk exaggeration; so the participants preferred to take advantage of EoU and speed despite the fact that they were aware of the risks.
Fractional Transmission Line with Losses
(2014) Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
In this manuscript, the fractional transmission line with losses is presented. The order of the Caputo derivative is considered as 0 < β ≤ 1 and 0 < γ ≤ 1 for the fractional equation in space and time domain, respectively. Two cases are solved, with fractional spatial and fractional temporal derivatives, and also numerical simulations were carried out, where there are taken both derivatives in simultaneous form. Two parameters σx and σt are introduced and a physical relation between these parameters is reported. Solutions in space and time are given in terms of the Mittag-Leffler functions. The classic cases are recovered when β and γ are equal to 1.
FractionalHybridDifferential EquationsandCoupled Fixed-Point Results for α-Admissible F(ψ1, ψ2) − Contractions in M − Metric Spaces
(2020) Karapınar, Erdal; Shimaa I., Moustafa; Shehata, Ayman; Agarwal, Ravi P.; 19184; Matematik
In this paper, we investigate the existence of a unique coupled fixed point for admissible mapping which is of contraction in the context of metric space. We have also shown that the results presented in this paper would extend many recent results appearing in the literature. Furthermore, we apply our results to develop sufficient conditions for the existence and uniqueness of a solution for a coupled system of fractional hybrid differential equations with linear perturbations of second type and with three-point boundary conditions.
Local fractional Sumudu decomposition method for linear partial differential equations with local fractional derivative
(Elsevier Science BV, 2019) Baleanu, Dumitru; Baleanu, Dumitru; Belghaba, Kacem; Cherif, Mountassir Hamdi; 56389; Matematik
In the paper, a combined form of the Sumudu transform method with the Adomian decomposition method in the sense of local fractional derivative, is proposed to solve fractional partial differential equations. This method is called the local fractional Sumudu decomposition method (LFSDM) and is used to describe the non-differentiable problems. It would be interesting to apply LFSDM to some well-known problems to see the benefits obtained. (C) 2017 The Authors. Production and hosting by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY-NC-ND license.
Numerical and Bifurcations Analysis for Multi Order Fractional Model of Hiv Infection of Cd4(+)T-Cells
(Univ Politehnica Bucharest, 2016) Baleanu, Dumitru; Arshad, Sadia; Baleanu, Dumitru; 56389; Matematik
In this paper, we solve the dynamical system of HIV infection of CD4(+) T cells within the multi-order fractional derivatives. The Bernstein operational matrices in arbitrary interval [a,b] are applied to obtain the approximate analytical solution of the model. In this way, the fractional differential equations are reduced to an algebraic easily solvable system. The obtained solutions are accurate and the method is very efficient and simple in implementation. With the help of bifurcation analysis, we acquired the critical value of viral death rate, that is, if viral death rate is greater than the critical value then level of virus particles starts to decline and thus free virus will eventually eliminate and patient is cured. Further, we found the threshold for viral infection rate analytically, which assures the stability of uninfected equilibrium and virus will ultimately eradicate.
On new traveling wave solutions of potential KdV and (3+1)-dimensional Burgers equations
(Int Scientific Research Publications, 2016) Baleanu, Dumitru; İnan, İbrahim E.; Uğurlu, Yavuz; İnç, Mustafa; Baleanu, Dumitru; 56389; Matematik
This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensional Burgers equation (BE) by the two variables (G'/G, 1/G) expansion method (EM). Obtained soliton solutions are designated in terms of kink, bell-shaped solitary wave, periodic and singular periodic wave solutions. These solutions may be useful and desirable to explain some nonlinear physical phenomena. (C) 2016 All rights reserved.
Optimal Approximation and Pricing of High- Dimensional Options
(Lambert Academic Publishing, 2019) Kushpel, Alexander; 279144; Matematik
The book introduces an original general approach to the problem of multidimensional pricing which is applicable for a wide range of practically important examples. It gives a comprehensive and self-contained treatment of the problem of multidimensional pricing which provides the reader with all technical details. The book reflects a new stage of research in Quantitative Finance. It gives a particular fascination when apparently disjoint areas turn out to have a meaningful connection to each other. It demonstrates on concrete examples deep connections between Quantitative Finance and Numerical Analysis, Topology, Functional Analysis and Complexity Theory. The book can be considered as an inspirational source for practitioners, graduate and postgraduate students, MSc and PhD projects, to those working in Quantitative Finance and Economics.
Spectrophotometry simultaneous determination of levamisole and triclabendazole in tablets by principal component regression and partial least squares chemometric methods
(2008) Baleanu, Dumitru; Dinç, Erdal; Baleanu, Dumitru; 56389; Matematik
Principal component regression (PCR) and partial least squares (PLS) chemometric methods were applied to the simultaneous quantitative analysis of levamisole (LVM) and triclabendazole (TCB) in tablets without using a preliminary separation, even in presence of the overlapping spectra of the above compounds. For both PCR and PLS, a concentration set containing 25 different mixtures of LVM and TCB in the linear concentration range was symmetrically prepared and then the absorbance values of the concentration set were measured at the wavelength set with Δλ=0.1 nm in the spectral region of 225-322.3 nm. PCR and PLS calibrations were obtained by applying the PCR and PLS algorithms to the concentration set data (y-block) and their corresponding absorbance data (x-block). The validity of PCR and PLS chemometric methods was performed by using the independent synthetic mixtures and the standard addition technique. Then, these analytical methods were applied to the commercial tablets and a good agreement was obtained between experimental results provided by the application of the PCR and PLS to the synthetic and real samples.

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