Fen - Edebiyat Fakültesi

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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; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 13
Citation - Scopus: 14
An Accurate Legendre Collocation Scheme for Coupled Hyperbolic Equations With Variable Coefficients
(Editura Acad Romane, 2014) Doha, E. H.; Baleanu, Dumitru; Bhrawy, A. H.; Baleanu, D.; Abdelkawy, M. A.; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The study of numerical solutions of nonlinear coupled hyperbolic partial differential equations (PDEs) with variable coefficients subject to initial-boundary conditions continues to be a major research area with widespread applications in modern physics and technology. One of the most important advantages of collocation method is the possibility of dealing with nonlinear partial differential equations (NPDEs) as well as PDEs with variable coefficients. A numerical solution based on a Legendre collocation method is extended to solve nonlinear coupled hyperbolic PDEs with variable coefficients. This approach, which is based on Legendre polynomials and Gauss-Lobatto quadrature integration, reduces the solving of nonlinear coupled hyperbolic PDEs with variable coefficients to a system of nonlinear ordinary differential equations that is far easier to solve. The obtained results show that the proposed numerical algorithm is efficient and very accurate.
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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.; 28932; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 85
Citation - Scopus: 116
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.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 30
Citation - Scopus: 33
Analysis of a New Fractional Model for Damped Bergers' Equation
(de Gruyter Open Ltd, 2017) Kumar, Devendra; Al Qurashi, Maysaa; Baleanu, Dumitru; Singh, Jagdev; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we present a fractional model of the damped Bergers' equation associated with the Caputo-Fabrizio fractional derivative. The numerical solution is derived by using the concept of an iterative method. The stability of the applied method is proved by employing the postulate of fixed point. To demonstrate the effectiveness of the used fractional derivative and the iterative method, numerical results are given for distinct values of the order of the fractional derivative.
Citation - WoS: 6
Citation - Scopus: 7
Analysis of Diffusivity Equation Using Differential Quadrature Method
(Editura Acad Romane, 2014) Razminia, K.; Baleanu, Dumitru; Razminia, A.; Kharrat, R.; Baleanu, D.; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Evaluation of exact analytical solution for flow to a well, under the assumptions made in its development commonly requires large amounts of computation time and can produce inaccurate results for selected combinations of parameters. Large computation times occur because the solution involves the infinite series. Each term of the series requires evaluation of exponentials and Bessel functions, and the series itself is sometimes slowly convergent. Inaccuracies can result from lack of computer precision or from the use of improper methods of numerical computation. This paper presents a computationally efficient and an accurate new methodology in differential quadrature analysis of diffusivity equation to overcome these difficulties. The methodology would overcome the difficulties in boundary conditions implementations of second order partial differential equations encountered in such problems. The weighting coefficients employed are not exclusive, and any accurate and efficient method such as the generalized differential quadrature method may be used to produce the method's weighting coefficients. By solving finite and infinite boundary condition in diffusivity equation and by comparing the results with those of existing solutions and/or those of other methodologies, accuracy, convergences, reduction of computation time, and efficiency of the methodology are asserted.
Citation - WoS: 4
Analysis of Drude Model Using Fractional Derivatives Without Singular Kernels
(de Gruyter Open Ltd, 2017) Rosales Garcia, J. Juan; Ortega Contreras, Abraham; Baleanu, Dumitru; Martinez Jimenez, Leonardo; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF), and fractional derivatives with a stretched Mittag-Leffer function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < gamma <= 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when gamma < 0.8.
Citation - WoS: 42
Citation - Scopus: 66
Analysis of Fractal Wave Equations by Local Fractional Fourier Series Method
(Hindawi Ltd, 2013) Baleanu, Dumitru; Yang, Xiao-Jun; Yang, Yong-Ju; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 36
Citation - Scopus: 46
Analysis of Keller-Segel Model With Atangana-Baleanu Fractional Derivative
(Univ Nis, Fac Sci Math, 2018) Baleanu, Dumitru; Celik, Ercan; Dokuyucu, Mustafa Ali; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The new definition of the fractional derivative was defined by Atangana and Baleanu in 2016. They used the generalized Mittag-Leffler function with the non-singular and non-local kernel. Further, their version provides all properties of fractional derivatives. Our aim is to analyse the Keller-Segel model with Caputo and Atangana-Baleanu fractional derivative in Caputo sense. Using fixed point theory, we first show the existence of coupled solutions. We then examine the uniqueness of these solutions. Finally, we compare our results numerically by modifying our model according to both definitions, and we demonstrate these results on the graphs in detail. All computations were done using Mathematica.
Citation - WoS: 46
Citation - Scopus: 49
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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 243
Analysis of Time-Fractional Hunter-Saxton Equation: a Model of Neumatic Liquid Crystal
(Sciendo, 2016) Baleanu, Dumitru; Alsaedi, Ahmed; Atangana, Abdon; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, a theoretical study of diffusion of neumatic liquid crystals was done using the concept of fractional order derivative. This version of fractional derivative is very easy to handle and obey to almost all the properties satisfied by the conventional Newtonian concept of derivative. The mathematical equation underpinning this physical phenomenon was solved analytically via the so-called homotopy decomposition method. In order to show the accuracy of this iteration method, we constructed a Hilbert space in which we proved its stability for the time-fractional Hunder-Saxton equation.
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.; 6981; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 6
Citation - Scopus: 6
Analytical Mathematical Schemes: Circular Rod Grounded Via Transverse Poisson's Effect and Extensive Wave Propagation on the Surface of Water
(de Gruyter Poland Sp Z O O, 2020) Seadawy, Aly R.; Baleanu, Dumitru; Ali, Asghar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This article scrutinizes the efficacy of analytical mathematical schemes, improved simple equation and exp(-Psi(xi))-expansion techniques for solving the well-known nonlinear partial differential equations. A longitudinal wave model is used for the description of the dispersion in the circular rod grounded via transverse Poisson's effect; similarly, the Boussinesq equation is used for extensive wave propagation on the surface of water. Many other such types of equations are also solved with these techniques. Hence, our methods appear easier and faster via symbolic computation.
Citation - WoS: 387
Citation - Scopus: 426
Anomalous Diffusion Expressed Through Fractional Order Differential Operators in the Bloch-Torrey Equation
(Academic Press inc Elsevier Science, 2008) Abdullah, Osama; Baleanu, Dumitru; Zhou, Xiaohong Joe; Magin, Richard L.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Diffusion weighted MRI is used clinically to detect and characterize neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion relies on d iffusi on -weighted pulse sequences to probe biophysical models of molecular diffusion-typically exp[-(bD)]-where D is the apparent diffusion coefficient (turn (2)/s) and b depends on the specific gradient pulse sequence parameters. Several recent studies have investigated the so-called anomalous diffusion stretched exponential model-exp[-(bD)(alpha)], where alpha is a measure of tissue complexity that can be derived from fractal models of tissue structure. In this paper we propose an alternative derivation for the stretched exponential model using fractional order space and time derivatives. First, we consider the case where the spatial Laplacian in the Bloch-Torrey equation is generalized to incorporate a fractional order Brownian model of diffusivity. Second, we consider the case where the time derivative in the Bloch-Torrey equation is replaced by a Riemann-Liouville fractional order time derivative expressed in the Caputo form. Both cases revert to the classical results for integer order operations. Fractional order dynamics derived for the first case were observed to fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Future developments of this approach may be useful for classifying anomalous diffusion in tissues with developing pathology. (c) 2007 Elsevier Inc. All rights reserved.
Citation - WoS: 81
Citation - Scopus: 90
Application of a Homogeneous Balance Method To Exact Solutions of Nonlinear Fractional Evolution Equations
(Asme, 2014) Tajadodi, H.; Baleanu, D.; Jafari, H.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The fractional Fan subequation method of the fractional Riccati equation is applied to construct the exact solutions of some nonlinear fractional evolution equations. In this paper, a powerful algorithm is developed for the exact solutions of the modified equal width equation, the Fisher equation, the nonlinear Telegraph equation, and the Cahn-Allen equation of fractional order. Fractional derivatives are described in the sense of the modified Riemann-Liouville derivative. Some relevant examples are investigated.
Citation - WoS: 6
Citation - Scopus: 8
Application of Anns Approach for Wave-Like and Heat-Like Equations
(de Gruyter Poland Sp Zoo, 2017) Baleanu, Dumitru; Jafarian, Ahmad; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Artificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.
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; 6981; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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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