Matematik Bölümü

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A Discussion On the Role of People in Global Software Development [Rasprava O Ulozi Ljudi U Globalnom Razvoju Softvera]
(2013) Misra, Sanjay; Colomo-Palacios, Ricardo; Pusatlı, Özgür Tolga; Soto-Acosta, Pedro
Literature is producing a considerable amount of papers which focus on the risks, challenges and solutions of global software development (GSD). However, the influence of human factors on the success of GSD projects requires further study. The aim of our paper is twofold. First, to identify the challenges related to the human factors in GSD and, second, to propose the solution(s), which could help in solving or reducing the overall impact of these challenges. The main conclusions of this research can be valuable to organizations that are willing to achieve the quality objectives regarding GSD projects.
Citation - WoS: 20
Citation - Scopus: 28
About Schrodinger Equation on Fractals Curves Imbedding in R ³
(Springer/plenum Publishers, 2015) Golmankhaneh, Ali Khalili; Baleanu, Dumitru; Golmankhaneh, Alireza Khalili
In this paper we introduced the quantum mechanics on fractal time-space. In a suggested formalism the time and space vary on Cantor-set and Von-Koch curve, respectively. Using Feynman path method in quantum mechanics and F (alpha) -calculus we find SchrA << dinger equation on on fractal time-space. The Hamiltonian and momentum fractal operator has been indicated. More, the continuity equation and the probability density is given in view of F (alpha) -calculus.
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.; Matematik
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: 34
Adaptive Fractional-Order Blood Glucose Regulator Based on High-Order Sliding Mode Observer
(inst Engineering Technology-iet, 2019) Heydarinejad, Hamid; Baleanu, Dumitru; Delavari, Hadi
Type I diabetes is described by the destruction of the insulin-producing beta-cells in the pancreas. Hence, exogenous insulin administration is necessary for Type I diabetes patients. In this study, to estimate the states that are not directly available from the Bergman minimal model a high-order sliding mode observer is proposed. Then fractional calculus is combined with sliding mode control (SMC) for blood glucose regulation to create more robustness performance and make more degree of freedom and flexibility for the proposed method. Then an adaptive fractional-order SMC is proposed. The adaptive SMC protect controller against disturbance and uncertainties while the fractional calculus provides robust performance. Numerical simulation verifies that the proposed controllers have better performance in the presence of disturbance and uncertainties without chattering.
Citation - Scopus: 9
Advanced Topics in Fractional Dynamics
(Hindawi Ltd, 2013) Srivastava, H. M.; Daftardar-Gejji, Varsha; Li, Changpin; Machado, J. A. Tenreiro; Baleanu, Dumitru
Citation - WoS: 3
Citation - Scopus: 5
Aeroelastic Optimization of the High Aspect Ratio Wing With Aileron
(Tech Science Press, 2022) Mahariq, Ibrahim; Ghadak, Farhad; Accouche, Oussama; Jarad, Fahd; Ghalandari, Mohammad
In aircraft wings, aileron mass parameter presents a tremendous effect on the velocity and frequency of the flutter problem. For that purpose, we present the optimization of a composite design wing with an aileron, using machine-learning approach. Mass properties and its distribution have a great influence on the multi-variate optimization procedure, based on speed and frequency of flutter. First, flutter speed was obtained to estimate aileron impact. Additionally mass-equilibrated and other features were investigated. It can deduced that changing the position and mass properties of the aileron are tangible following the speed and frequency of the wing flutter. Based on the proposed optimization method, the best position of the aileron is determined for the composite wing to postpone flutter instability and decrease the existed stress. The represented coupled aero-structural model is emerged from subsonic aerodynamics model, which has been developed using the panel method in multidimensional space. The structural modeling has been conducted by finite element method, using the p-k method. The fluid -structure equations are solved and the results are extracted.
Citation - WoS: 12
Citation - Scopus: 13
Al2o3 and Γal2o3 Nanomaterials Based Nanofluid Models With Surface Diffusion: Applications for Thermal Performance in Multiple Engineering Systems and Industries
(Tech Science Press, 2021) Khan, Umar; Ahmed, Naveed; Mohyud-Din, Syed Tauseef; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Nan, Adnan
Thermal transport investigation in colloidal suspensions is taking a significant research direction. The applications of these fluids are found in various industries, engineering, aerodynamics, mechanical engineering and medical sciences etc. A huge amount of thermal transport is essential in the operation of various industrial production processes. It is a fact that conventional liquids have lower thermal transport characteristics as compared to colloidal suspensions. The colloidal suspensions have high thermal performance due to the thermophysical attributes of the nanoparticles and the host liquid. Therefore, researchers focused on the analysis of the heat transport in nanofluids under diverse circumstances. As such, the colloidal analysis of H2O composed by gamma Al2O3 and Al2O3 is conducted over an elastic cylinder. The governing flow models of gamma Al2O3/H2O and Al2O3/H2O is reduced in the dimensionless form by adopting the described similarity transforms. The colloidal models are handled by implementing the suitable numerical technique and provided the results for the velocity, temperature and local thermal performance rate against the multiple flow parameters. From the presented results, it is shown that the velocity of Al(2)O3-H2O increases promptly against a high Reynolds number and it decreases for high-volume fraction. The significant contribution of the volumetric fraction is examined for thermal enhancement of nanofluids. The temperature of Al2O3-H2O and gamma Al2O3-H-2O significantly increases against a higher phi. Most importantly, the analysis shows that gamma Al2O3-H2O has a high local thermal performance rate compared to Al2O3-H2O. Therefore, it is concluded that gamma Al2O3-H2O is a better heat transfer fluid and is suitable for industrial and technological uses.
Algebraic Integration of Sigma-Model Field Equations
(Springer, 2009) Yilmaz, N. T.
We prove that the dualization algebra of the sigma model with a symmetric coset space is a Lie algebra and show that it generates an appropriate adjoint representation that allows integrating the field equations locally, which yields first-order equations.
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; Matematik
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.
Ample Spectrum Contractions in Branciari Distance Spaces
(Yokohama Publ, 2021) Karapinar, Erdal; Karapınar, Erdal; Lopez de Hierro, Antonio Francisco Roldan; Shahzad, Naseer; Matematik
Very recently, the notion of ample spectrum contraction has been introduced in order to unify, under the same axioms, a large number of contractive mappings that have had great success in the field of Fixed Point Theory in recent years and that have been used in a wide variety of applications in Nonlinear Analysis (Meir-Keeler contractions, Geragthy contractions, contractions under simulation functions, contractions under R-functions, etc.) However, the subtle conditions that define ample spectrum contractions cannot be extended as they are to new kinds of abstract metric spaces because they involve key properties that are only fulfilled in metric spaces. In this paper, based on a very recent work in which the authors unravel the essential properties of the topology in Branciari spaces, we investigate the reasons why the proposed axiomatic fails in Branciari spaces and we illustrate how to overcome such drawbacks. As a consequence, we characterize the notion of ample spectrum contraction in the setting of Branciari distance spaces and we also investigate the existence and uniqueness of fixed points for such family of contractions in the context of complete Branciari distance spaces.
Citation - WoS: 85
Citation - Scopus: 119
Analysis and Dynamics of Fractional Order Mathematical Model of Covid-19 in Nigeria Using Atangana-Baleanu Operator
(Tech Science Press, 2021) Shaikh, Amjad S.; Ibrahim, Mohammed O.; Nisar, Kottakkaran Sooppy; Baleanu, Dumitru; Khan, Ilyas; Abioye, Adesoye I.; Peter, Olumuyiwa J.
We propose a mathematical model of the coronavirus disease 2019 (COVID-19) to investigate the transmission and control mechanism of the disease in the community of Nigeria. Using stability theory of differential equations, the qualitative behavior of model is studied. The pandemic indicator represented by basic reproductive number R-0 is obtained from the largest eigenvalue of the next-generation matrix. Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease. Further, we examined this model by using Atangana-Baleanu fractional derivative operator and existence criteria of solution for the operator is established. We consider the data of reported infection cases from April 1, 2020, till April 30, 2020, and parameterized the model. We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations. The impacts of various biological parameters on transmission dynamics of COVID-19 is examined. These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease. In the end, the obtained results are demonstrated graphically to justify our theoretical findings.
Citation - WoS: 18
Citation - Scopus: 24
Analysis for Fractional-Order Predator-Prey Model With Uncertainty
(inst Engineering Technology-iet, 2019) Baleanu, Dumitru; Thangapandi, Kalidas; Perera, Shyam Sanjeewa Nishantha; Narayanamoorthy, Samayan
Here, the authors analyse the fractional-order predator-prey model with uncertainty, due to the vast applications in various ecological systems. The most of the ecological model do not have exact analytic solution, so they proposed a numerical technique for an approximate solution. In the proposed method, they have implemented the higher order term into the fractional Euler method to enhance the precise solution. Further, the present attempt is aimed to discuss the solutions of the FPPM with uncertainty (fuzzy) initial conditions. The initial conditions of the predator-prey model were taken as fuzzy initial conditions due to the fact that the ecological model highly depends on uncertain parameters such as growth/decay rate, climatic conditions, and chemical reactions. Finally, the numerical example manifest that the proposed method is authentic, applicable, easy to use from a computational viewpoint and the acquired outcomes are balanced with the existing method (HPM), which shows the efficiency of the proposed method.
Citation - WoS: 42
Citation - Scopus: 67
Analysis of Fractal Wave Equations by Local Fractional Fourier Series Method
(Hindawi Ltd, 2013) Baleanu, Dumitru; Yang, Xiao-Jun; Yang, Yong-Ju
The fractal wave equations with local fractional derivatives are investigated in this paper. The analytical solutions are obtained by using local fractional Fourier series method. The present method is very efficient and accurate to process a class of local fractional differential equations.
Citation - WoS: 48
Citation - Scopus: 52
Analysis of Logistic Equation Pertaining To a New Fractional Derivative With Non-Singular Kernel
(Sage Publications Ltd, 2017) Singh, Jagdev; Al Qurashi, Maysaa; Baleanu, Dumitru; Kumar, Devendra
In this work, we aim to analyze the logistic equation with a new derivative of fractional order termed in Caputo-Fabrizio sense. The logistic equation describes the population growth of species. The existence of the solution is shown with the help of the fixed-point theory. A deep analysis of the existence and uniqueness of the solution is discussed. The numerical simulation is conducted with the help of the iterative technique. Some numerical simulations are also given graphically to observe the effects of the fractional order derivative on the growth of population.
Citation - WoS: 9
Citation - Scopus: 10
Analysis of the Effect of Potential Cycles on the Reflective Infrared Signals of Nitro Groups in Nanofilms: Application of the Fractional Moments Statistics
(Wiley-v C H verlag Gmbh, 2010) Alekhin, Alexander P.; Baleanu, Dumitru; Dinc, Erdal; Ustundag, Zafer; Eksi, Haslet; Solak, Ali Osman; Nigmatulin, Raoul R.
The effect of the potential cycles on the reflective IR signals of nitro-groups in nanofilms was studied for the statistical characterization of nitrobenzene (NB) and nitroazobenzene (NAB)-modified glassy carbon (GC) surfaces. Both NB and NAB nanofilms were obtained by the electrochemical reduction of the diazonium tetrafluoroborate salts in acetonitrile using cyclic voltammetry (CV). The modified surfaces were denoted as GC-(NB)(n) and GC-(NAB)(n), respectively, where n indicates the number of CV cycles performed during modification. Reflective IR signals of the normalized NB and NAB nanofilms and GC were used for the quantitative evaluation of the effect of the potential cycles on the reflective IR signals of nitro-groups in nanofilms. The detection and quantitative 'reading' of the influence of number of CV cycles were realized in the frame of a new error controllable approach that was applied for analysis of all available set of data. This approach includes in itself the following basic steps: (a) the procedure of the division (normalization) on the GC spectra, (b) the comparison of the smoothed spectra for their statistical proximity in the frame of the statistics of the fractional moments, (c) extraction of possible calibration parameters for possible calibration of the normalized spectra with respect to the number of CV cycles. These three basic steps are becoming effective for detection of the influence of some external factors. In our case it is important to detect the influence of the factor n characterizing CV cycles.
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
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: 4
Citation - Scopus: 6
Analysis of Uv Spectral Bands Using Multidimensional Scaling
(Springer London Ltd, 2015) Dinc, Erdal; Baleanu, Dumitru; Tenreiro Machado, J. A.
This study describes the change of the ultraviolet spectral bands starting from 0.1 to 5.0 nm slit width in the spectral range of 200-400 nm. The analysis of the spectral bands is carried out by using the multidimensional scaling (MDS) approach to reach the latent spectral background. This approach indicates that 0.1 nm slit width gives higher-order noise together with better spectral details. Thus, 5.0 nm slit width possesses the higher peak amplitude and lower-order noise together with poor spectral details. In the above-mentioned conditions, the main problem is to find the relationship between the spectral band properties and the slit width. For this aim, the MDS tool is to used recognize the hidden information of the ultraviolet spectra of sildenafil citrate by using a Shimadzu UV-VIS 2550, which is in the world the best double monochromator instrument. In this study, the proposed mathematical approach gives the rich findings for the efficient use of the spectrophotometer in the qualitative and quantitative studies.
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.
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: 9
Analytic Study of Allen-Cahn Equation of Fractional Order
(int Center Scientific Research & Studies, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; Matematik
The key purpose of the present article is to analyze the Allen Cahn equation of fractional order. The fractional Allen-Cahn equation models the process of phase separation in iron alloys, along with order-disorder transitions. The analytical technique is employed to investigate the fractional model of Allen-Cahn equation. The numerical results are shown graphically. The outcomes show that the analytical technique is very efficient and user friendly for handling nonlinear fractional differential equations describing the real world problems.
Citation - WoS: 3
Citation - Scopus: 4
Application of Continuous Wavelet Transform To the Analysis of the Modulus of the Fractional Fourier Transform Bands for Resolving Two Component Mixture
(Springer London Ltd, 2015) Duarte, Fernando B.; Machado, J. A. Tenreiro; Baleanu, Dumitru; Dinc, Erdal
In this paper, the fractional Fourier transform (FrFT) is applied to the spectral bands of two component mixture containing oxfendazole and oxyclozanide to provide the multicomponent quantitative prediction of the related substances. With this aim in mind, the modulus of FrFT spectral bands are processed by the continuous Mexican Hat family of wavelets, being denoted by MEXH-CWT-MOFrFT. Four modulus sets are obtained for the parameter of the FrFT going from 0.6 up to 0.9 in order to compare their effects upon the spectral and quantitative resolutions. Four linear regression plots for each substance were obtained by measuring the MEXH-CWT-MOFrFT amplitudes in the application of the MEXH family to the modulus of the FrFT. This new combined powerful tool is validated by analyzing the artificial samples of the related drugs, and it is applied to the quality control of the commercial veterinary samples.

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