Fen - Edebiyat Fakültesi

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Citation - WoS: 64
Citation - Scopus: 63
An Accurate Numerical Technique for Solving Fractional Optimal Control Problems
(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Doha, E. H.; Baleanu, D.; Ezz-Eldien, S. S.; Abdelkawy, M. A.; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we propose the shifted Legendre orthonormal polynomials for the numerical solution of the fractional optimal control problems that appear in several branches of physics and engineering. The Rayleigh-Ritz method for the necessary conditions of optimization and the operational matrix of fractional derivatives are used together with the help of the properties of the shifted Legendre orthonormal polynomials to reduce the fractional optimal control problem to solving a system of algebraic equations that greatly simplifies the problem. For confirming the efficiency and accuracy of the proposed technique, an illustrative numerical example is introduced with its approximate solution.
Citation - WoS: 3
Citation - Scopus: 5
Adomian-Pade Approximate Solutions To the Conformable Non-Linear Heat Transfer Equation
(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This paper adopts the Adomian decomposition method and the Pade approximation technique to derive the approximate solutions of a conformable heat transfer equation by considering the new definition of the Adomian polynomials. The Pade approximate solutions are derived along with interesting figures showing the approximate solutions.
Citation - WoS: 5
Citation - Scopus: 7
An Adoptive Renewable Energy Resource Selection Using Hesitant Pythagorean Fuzzy Dematel and Vikor Methods
(Ios Press, 2022) Narayanamoorthy, Samayan; Kang, Daekook; Baleanu, Dumitru; Geetha, Selvaraj; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Nowadays, energy from renewable energy resources (RERs) partially satisfies society's energy demands. Investment in the renewable energy system is an arduous task because of huge investments. Generally, RERs selection involves conflicting criteria. Hence there is necessary to evaluate the RERs alternatives in economic, technological, and environmental aspects. Here, DEMATEL (Decision Making Trial and Evaluation Laboratory) method has been utilized to assess the interrelationship among the criteria under hesitant Pythagorean fuzzy (HPF) information. The Pythagorean fuzzy set (PFS) has recently obtained enormous attention and is applied widely in decision-making. We have proposed an integrating model with DEMATEL and VIKOR (Vise Kriterijumska Optimizacija Kompromisno Resenje) methods to identify and evaluate the criteria and alternatives in RERs selection. Within the proposed model, the HPF-DEMATEL method is utilized for weighting the criteria, and the HPF-VIKOR method is utilized for ranking. Finally, an illustrative example demonstrates the proposed method.
Advanced Modelling of Transport Problems in Heat-Mass and Related Fluid Mechanics
(Vinca inst Nuclear Sci, 2021) Hristov, Jordan; Baleanu, Dumitru; Kumar, Devendra; Baleanu, Dumitru; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 3
Alternative Approaches To the Spectral Quantitative Resolution of Two-Component Mixture by Wavelet Families
(Soc Chilena Quimica, 2009) Dinc, Erdal; Baleanu, Dumitru; Arslan, Fahrettin; Baleanu, Dumitru; 6981; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A new spectral continuous wavelet transform (CWT) methods are proposed for the quantitative analysis of the binary mixtures. The simultaneous spectral resolution of binary mixtures and tablets containing paracetamol (PAR) and chloroxozone (CHL) with overlapping absorption spectra is performed by six wavelet families with no chemical separation procedure. The calibration graphs for the six wavelet families are obtained by the help of the data collected from the CWT-signal amplitudes corresponding to the zero crossing points in the spectral range of 210 nm-310 nm. The validation of each wavelet family is carried out by analyzing various synthetic binary mixtures of the above mentioned drugs. The second derivative spectrophotometry (D2) is used to compare the experimental results provided by the analyzed continuous wavelet families and a good coincidence is reported for the proposed analytical approaches.
Citation - WoS: 12
Citation - Scopus: 12
Analysis of Fractional Non-Linear Diffusion Behaviors Based on Adomian Polynomials
(Vinca inst Nuclear Sci, 2017) Baleanu, Dumitru; Luo, Wei-Hua; Wu, Guo-Cheng; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
A 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.
Citation - WoS: 8
Citation - Scopus: 13
Analysis of Riccati Differential Equations Within a New Fractional Derivative Without Singular Kernel
(Ios Press, 2017) Lia, Atena; Tejadodi, Haleh; Baleanu, Dumitru; Jafari, Hossein; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Recently Caputo and Fabrizio suggested new definition of fractional derivative that the new kernel has no singularity. In this paper, an analytical method for solving Riccati differential equation with a new fractional derivative is reported. We present numerical results of solving the fractional Riccati differential equations by using the variational iteration method and its modification. The obtained results of two methods demonstrate the efficiency and simplicity of the MVIM that gives good approximations for a larger interval.
Citation - WoS: 7
Citation - Scopus: 13
Analysis of the Impact of Thermal Radiation and Velocity Slip on the Melting of Magnetic Hydrodynamic Micropolar Fluid-Flow Over an Exponentially Stretching Sheet
(Vinca inst Nuclear Sci, 2023) Singh, Jagdev; Mehta, Ruchika; Kumar, Devendra; Baleanu, Dumitru; Kumar, Ravindra; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The belongings of radiation and velocity slip on MHD stream and melting warmth transmission of a micropolar liquid over an exponentially stretched sheet which is fixed in a porous medium with heat source/sink are accessible. Homothety trans-forms the major PDE into a set of non-linear ODE. Then, by varying the boundary value problem to the initial value problem first, we get a numerical solution the non-linear system of equations. It has been observed that related parameters have a significant effect on flow and heat transfer characteristics, which are demonstrat-ed and explained in aspect done their figures. Velocity and temperature decrease by an extension in the magnetic aspect, and the angular velocity increase but the reverse effects come in melting, microrotation, and mixed convection parameters. The surface resistance coefficient as well as couple stress both decreases with amplification in the Eckert number microrotation, material, radiation, and heat source/sink parameter but the heat transport coefficient increase.
Citation - WoS: 2
Citation - Scopus: 2
Analysis of the New Technique To Solution of Fractional Wave- and Heat-Like Equation
(Jagiellonian Univ Press, 2017) Agheli, Bahram; Darzi, Rahmat; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We have applied the new approach of homotopic perturbation method (NHPM) for wave- and heat-like equation featuring time-fractional derivative. A combination of NHPM and multiple fractional power series form has been used the first time to present analytical solution. In order to illustrate the simplicity and ability of the suggested approach, some specific and clear examples have been given. All computations were done using Mathematica.
Citation - WoS: 5
Citation - Scopus: 6
Analytic Solution for a Nonlinear Problem of Magneto-Thermoelasticity
(Pergamon-elsevier Science Ltd, 2013) Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; Jafarian, A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we present a comparative study of the homotopy analysis method (HAM), the variational iteration method (VIM) and the iterative method (He's polynomials). The approximate solution of the coupled harmonic waves nonlinear magneto-thermoelasticity equations under influence of rotation is obtained. In order to control and adjust the convergence region and the rate of solution series, we show that it is possible to choose a valid auxiliary parameter h of HAM. Using the boundary and the initial conditions we select a suitable initial approximation. The results show that these methods are very efficient, convenient and applicable to a large class of problems.
Citation - WoS: 15
Citation - Scopus: 16
Application of Haar and Mexican Hat Wavelets To Double Divisor-Ratio Spectra for the Multicomponent Determination of Ascorbic Acid, Acetylsalicylic Acid and Paracetamol in Effervescent Tablets
(Soc Brasileira Quimica, 2008) Baleanu, Dumitru; Dinc, Erdal; 6981; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Simultaneous determination of ascorbic acid (AA), acetylsalicylic acid (ASP) and paracetamol (PAR) in their synthetic mixtures and effervescent tablets were performed by Haar and Mexican continuous wavelet transforms (HAAR-CWT and MEXH-CWT, respectively) together with double divisor technique. The signal processing methods are based on the application of HAAR-CWT and MEXH-CWT to the double divisor-ratio spectra (DDRS). These spectra were obtained by dividing the absorption spectra of pure compound and its ternary mixtures by a double-divisor or standard spectrum corresponding to a mixture of two compounds in ternary mixture. A combined use of HAAR-CWT and MEXH-CWT with double divisor-ratio spectra (DDRS) was denoted by DDRS-HAAR CWT and DDRS-MEXH CWT. To check the ability or applicability of the developed DDRS-CWT methods, the double divisor-ratio spectra-derivative spectrophotometric (DDRS-DS) method, as a comparison method, was applied to the above mentioned samples containing AA, ASP and PAR and satisfactory results were obtained.
Citation - WoS: 4
Citation - Scopus: 4
Approximate Controllability of Second-Order Nonlocal Impulsive Functional Integro-Differential Systems in Banach Spaces
(Korean Mathematical Soc, 2018) Arjunan, Mani Mallika; Nagaraj, Mahalingam; Suganya, Selvaraj; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This manuscript is involved with a category of second-order impulsive functional integro-differential equations with nonlocal conditions in Banach spaces. Sufficient conditions for existence and approximate controllability of mild solutions are acquired by making use of the theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem. An illustration is additionally furnished to prove the attained principles.
Citation - WoS: 2
Citation - Scopus: 2
Approximate Solutions and Conservation Laws of the Periodic Base Temperature of Convective Longitudinal Fins in Thermal Conductivity
(Vinca inst Nuclear Sci, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, the residual power series method is used to study the numerical approximations of a model of oscillating base temperature processes occurring in a convective rectangular fin with variable thermal conductivity. It is shown that the residual power series method is efficient for examining numerical behavior of non-linear models. Further, the conservation of heat is studied using the multiplier method.
Citation - WoS: 105
Citation - Scopus: 111
Approximate Solutions for Diffusion Equations on Cantor Space-Time
(Editura Acad Romane, 2013) Yang, Xiao-Jun; Baleanu, Dumitru; Baleanu, Dumitru; Zhong, Wei-Ping; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper we investigate diffusion equations on Cantor space-time and we obtain approximate solutions by using the local fractional Adomian decomposition method derived from the local fractional operators. Analytical solutions are given in terms of the Mittag-Leffler functions defined on Cantor sets.
Citation - WoS: 3
Citation - Scopus: 9
Artificial Intelligence Computing Analysis of Fractional Order Covid-19 Epidemic Model
(Aip Publishing, 2023) Baleanu, Dumitru; Cheema, Tahir Nawaz; Fadhal, Emad; Ibrahim, Rashid I. H.; Abdelli, Nouara; Raza, Ali; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Artificial intelligence plays a very prominent role in many fields, and of late, this term has been gaining much more popularity due to recent advances in machine learning. Machine learning is a sphere of artificial intelligence where machines are responsible for doing daily chores and are believed to be more intelligent than humans. Furthermore, artificial intelligence is significant in behavioral, social, physical, and biological engineering, biomathematical sciences, and many more disciplines. Fractional-order modeling of a real-world problem is a powerful tool for understanding the dynamics of the problem. In this study, an investigation into a fractional-order epidemic model of the novel coronavirus (COVID-19) is presented using intelligent computing through Bayesian-regularization backpropagation networks (BRBFNs). The designed BRBFNs are exploited to predict the transmission dynamics of COVID-19 disease by taking the dataset from a fractional numerical method based on the Grunwald-Letnikov backward finite difference. The datasets for the fractional-order mathematical model of COVID-19 for Wuhan and Karachi metropolitan cities are trained with BRBFNs for biased and unbiased input and target values. The proposed technique (BRBFNs) is implemented to estimate the integer and fractional-order COVID-19 spread dynamics. Its reliability, effectiveness, and validation are verified through consistently achieved accuracy metrics that depend on error histograms, regression studies, and mean squared error.
Citation - WoS: 3
Citation - Scopus: 3
Automorphisms of Braid Groups on Closed Surfaces Which Are Not S², T², P² or the Klein Bottle
(World Scientific Publ Co Pte Ltd, 2006) Zhang, Ping; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Consider a surface braid group of n strings as a subgroup of the isotopy group of homeomorphisms of the surface permuting n fixed distinguished points. Each automorphism of the surface braid group (respectively, of the special surface braid group) is shown to be a conjugate action on the braid group (respectively, on the special braid group) induced by a homeomorphism of the underlying surface if the closed surface, either orientable or non-orientable, is of negative Euler characteristic. In other words, the group of automorphisms of such a surface braid group is isomorphic to the extended mapping class group of the surface with n punctures, while the outer automorphism group of the surface braid group is isomorphic to the extended mapping class group of the closed surface itself.
Citation - WoS: 26
Citation - Scopus: 28
Boride Layer Growth Kinetics of Aisi H13 Steel Borided With Nano-Sized Powders
(Polska Akad Nauk, Polish Acad Sciences, inst Metall & Mater Sci Pas, 2018) Kanca, E.; Yilmaz, E.; Karakas, M. S.; Gunen, A.; 01. Çankaya Üniversitesi; 06. Mühendislik Fakültesi; 06.07. Malzeme Bilimi ve Mühendisliği
Growth kinetics of boride layers in AISI H13 steel was investigated using the pack bonding method at temperatures of 1073, 1173 and 1273 K (800 degrees C, 900 degrees C and 1000 degrees C) for periods of 2, 4 and 6 h with nano-sized boron (NB) and micron-sized Ekabor II powders as bonding agents. The total thickness of the boride layer (including both FeB and Fe2B) after boriding at 1273 K (1000 degrees C) for 6 h was 103.8 gm and 96.5 mu m for the NB and Ekabor II specimens, respectively. X-ray diffraction analysis of the boride layers on the surfaces borided with NB and Ekabor II revealed the presence of FeB and Fe2B phases with sawtooth morphology. The FeB/Fe2B volume ratio was higher in the specimens borided with NB. The thickness of the boride layer (FeB + Fe2B) increased with the increasing boriding temperature and time. The FeB layer in the NB specimen displayed a (002) preferred orientation.
The Bright and Dark Sides of Work Life" Tpd Work and Organizational Psychology Special Issue
(Turkish Psychologists Assoc, 2019) Sumer, H. Canan; Goncu-Kose, Asli; Toker, Yonca; Ok, A. Basak; Gokalp, Aysu; Mete, Ipek; Demircioglu, Zeynep Isil; 166202; 01. Çankaya Üniversitesi; 02. Fen-Edebiyat Fakültesi; 02.04. Psikoloji
Citation - WoS: 10
Citation - Scopus: 9
Bright, Dark, and Singular Optical Soliton Solutions for Perturbed Gerdjikov-Ivanov Equation
(Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Kumar, Sunil; Ulutas, Esma; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This study consider Gerdjikov-Ivanov equation where the perturbation terms appear with full non-linearity. The Jacobi elliptic function ansatz method is implemented to obtain exact solutions of this equation that models pulse dynamics in optical fibers. It is retrieved some bright, dark optical and singular solitons profile in the limiting cases of the Jacobi elliptic functions. The constraint conditions depending on the parameters for the existence of solitons are also presented.
Citation - Scopus: 1
Bullying as a Group Process: Investigation of Participant Roles in Terms of Social Status and Gender
(Turkish Psychologists Assoc, 2015) Topcu, Aysun Ergul; Donmez, Ali; 173556; 01. Çankaya Üniversitesi
This study mainly aims to test the participant roles approach on Turkish sample suggesting that bullying is a group process. In this regard, students' ways of involving in bullying and the extent to which children are aware of their participant roles and whether these participant roles differentiate in terms of gender and social status was investigated. A total of 774 students (384 females and 390 males), from 6(th), 7(th) and 8(th) grades of 11 different primary schools in Ankara participated in the study. The results showed that 74% of all children involved in one of the participant roles as bully (11.5%), assistant-reinforcer (10.9%), defender (21.1%), outsider (20.9%) and victim (9.7%). The examinations of the relations between self-reported and peer-reported scores of participant roles revealed that children were aware of their roles in the bullying situations, however, they significantly underestimated their roles in bully and assistant-reinforcer scales while overestimated their roles in the defender and outsider scales. Boys are more actively involved in bullying process than girls; boys participated most frequently in the roles of bully, assistant-reinforcer and victim while girls participated most frequently in the defender and outsider roles. In terms of the findings related to social status, victims were the least accepted and most rejected group among their peers although they did not differentiate from bullies and assistant-reinforcer in this sense. Besides, the victims were

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