Fen - Edebiyat Fakültesi

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Citation Count: Baleanu, Dumitru; Guler Y., "2D gravity and the Hamilton-Jacobi formalism" Nuovo Cimento Della Societa Italiana Di Fisica B-Basic Topics In Physics, Vol.117, No.8, pp.917-923, (2002)
2D gravity and the Hamilton-Jacobi formalism
(Soc Italiana Fisica, 2002-08) Baleanu, Dumitru; Güler, Yılmaz; 56389; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi,Matematik Bölümü
Hamilton-Jacobi formalism is used to study 2D gravity and its SL(2, R) hidden symmetry. If the contribution of the surface term is considered, the obtained results coincide with those given by the Dirac and Faddeev-Jackiw approaches.
Citation Count: Babakhani,A., Abdeljawad, T. (2013). A caputo fractional order boundary value problem with integral boundary conditions. Journal of Computational Analysis and Application, 15(4), 753-763.
A caputo fractional order boundary value problem with integral boundary conditions
(Eudoxus Press, 2013-05) Babakhani, Azizollah; Abdeljawad, Thabet; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü
In this paper, we discuss existence and uniqueness of solutions to nonlinear fractional order ordinary differential equations with integral boundary conditions in an ordered Banach space. We use the Caputo fractional differential operator and the nonlinearity depends on the fractional derivative of an unknown function. The nonlinear alternative of the Leray- Schauder type Theorem is the main tool used here to establish the existence and the Banach contraction principle to show the uniqueness of the solution under certain conditions. The compactness of solutions set is also investigated and an example is included to show the applicability of our results.
Citation Count: Baleanu, Dumitru; Defterli, Özlem; Agrawal, Om.P., "A central difference numerical scheme for fractional optimal control problems", Journal Of Vibration And Control, Vol.15, No.4, pp.583-597, (2009).
A central difference numerical scheme for fractional optimal control problems
(Sage Publications LTD, 2009-04) Baleanu, Dumitru; Defterli, Özlem; Agrawal, Om. P.; 56389; 31401; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
This paper presents a modified numerical scheme for a class of fractional optimal control problems where a fractional derivative (FD) is defined in the Riemann-Liouville sense. In this scheme, the entire time domain is divided into several sub-domains, and a FD at a time node point is approximated using a modified Grunwald-Letnikov approach. For the first-order derivative, the proposed modified Grunwald-Letnikov definition leads to a central difference scheme. When the approximations are substituted into the fractional optimal control equations, it leads to a set of algebraic equations which are solved using a direct numerical technique. Two examples, one time-invariant and the other time-variant, are considered to study the performance of the numerical scheme. Results show that 1) as the order of the derivative approaches an integer value, these formulations lead to solutions for the integer-order system, and 2) as the sizes of the sub-domains are reduced, the solutions converge. It is hoped that the present scheme would lead to stable numerical methods for fractional differential equations and optimal control problems.
Citation Count: Bhrawy, A.H...et al. (2016). A chebyshev-laguerre-gauss-radau collocation scheme for solving a time fractional sub-diffusion equation on a semi-infinite domain. Proceedings Of The Romanian Academy Series A-Mathematics Physics Technical Science Information Science, 16(4), 490-498.
A chebyshev-laguerre-gauss-radau collocation scheme for solving a time fractional sub-diffusion equation on a semi-infinite domain
(The Publishing House of the Romanian Academy, 2015) Bhrawy, A. H.; Abdelkawy, M. A.; Alzahrani, A. A.; Baleanu, Dumitru; Alzahrani, Ebraheem; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü
We propose a new efficient spectral collocation method for solving a time fractional sub-diffusion equation on a semi-infinite domain. The shifted Chebyshev-Gauss-Radau interpolation method is adapted for time discretization along with the Laguerre-Gauss-Radau collocation scheme that is used for space discretization on a semi-infinite domain. The main advantage of the proposed approach is that a spectral method is implemented for both time and space discretizations, which allows us to present a new efficient algorithm for solving time fractional sub-diffusion equations
Citation Count: Baleanu, Dumitru; Restrepo, Joel E.; Suragan, Durvudkhan (2021). "A class of time-fractional Dirac type operators", Chaos Solitons & Fractals, Vol. 143.
A class of time-fractional Dirac type operators
(2021-02) Baleanu, Dumitru; Restrepo, Joel E.; Suragan, Durvudkhan; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
By using a Witt basis, a new class of time-fractional Dirac type operators with time-variable coefficients is introduced. These operators lead to considering a wide range of fractional Cauchy problems. Solutions of the considered general fractional Cauchy problems are given explicitly. The representations of the solutions can be used efficiently for analytic and computational purposes. We apply the obtained representation of a solution to recover a variable coefficient solution of an inverse fractional Cauchy problem. Some concrete examples are given to show the diversity of the obtained results. (c) 2020 Elsevier Ltd. All rights reserved.
Citation Count: Abdeljawad, Thabet; Karapinar, E. (2011). "A common fixed point theorem of a Greguš type on convex cone metric spaces", Journal of Computational Analysis and Applications, Vol.13, No.4, pp.609-621.
A common fixed point theorem of a Greguš type on convex cone metric spaces
(2011) Abdeljawad, Thabet; Karapinar, Erdal; 19184; Çankaya Üniversitesi, Fen-Edebiyat Fakültesi, Matematik Bölümü
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.
Citation Count: Abdeljawad, T., Karapınar, E. (2011). A common fixed point theorem of a Gregus type on convex cone metric spaces. Journal of Computational Analysis and Applications, 13(4), 609-621.
A common fixed point theorem of a Gregus type on convex cone metric spaces
(Eudoxus Press, 2011-05) Abdeljawad, Thabet; Karapınar, Erdal; 19184; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü
The result of Ciric [1] on a common fixed point theorem of Gregus-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
Citation Count: Esen, Ziya; Butev, Ezgi; Karakas, M. Serdar, "A comparative study on biodegradation and mechanical properties of pressureless infiltrated Ti/Ti6Al4V-Mg composites", Journal of the Mechanical Behavior of Biomedical Materials, Vol. 63, pp. 273-283,(2016).
A comparative study on biodegradation and mechanical properties of pressureless infiltrated Ti/Ti6Al4V-Mg composites
(Elsevier Science BV, 2016-10) Esen, Ziya; Bütev, Ezgi; Karakaş, Mustafa Serdar; 52373; 47423; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
The mechanical response and biodegradation behavior of pressureless Mg-infiltrated Ti-Mg and Ti6Al4V-Mg composites were investigated by compression and simulated body fluid immersion tests, respectively. Prior porous preforms were surrounded uniformly with magnesium as a result of infiltration and the resultant composites were free of secondary phases and intermetallics. Although the composites' compressive strengths were superior compared to bone, both displayed elastic moduli similar to that of cortical bone and had higher ductility with respect to their starting porous forms. However, Ti-Mg composites were unable to preserve their mechanical stabilities during in-vitro tests such that they fractured in multiple locations within 15 days of immersion. The pressure generated by H-2 due to rapid corrosion of magnesium caused failure of the Ti-Mg composites through sintering necks. On the other hand, the galvanic effect seen in Ti6Al4V-Mg was less severe compared to that of Ti-Mg. The degradation rate of magnesium in Ti6Al4V-Mg was slower, and the composites were observed to be mechanically stable and preserved their integrities over the entire 25-day immersion test. Both composites showed bioinert and biodegradable characteristics during immersion tests and magnesium preferentially corroded leaving porosity behind while Ti/Ti6Al4V remained as a permanent scaffold. The porosity created by degradation of magnesium was refilled by new globular agglomerates. Mg(OH)(2) and CaHPO4 phases were encountered during immersion tests while MgCl2 was detected during only the first 5 days. Both composites were classified as bioactive since the precipitation of CaHPO4 phase is known to be precursor of hydroxyapatite formation, an essential requirement for an artificial material to bond to living bone. (C) 2016 Elsevier Ltd. All rights reserved.
A Computationally Efficient Method For a Class of Fractional Variational and Optimal Control Problems Using Fractional Gegenbauer Functions
(Editura Academiei Romane, 2018) El-Kalaawy, Ahmed A.; Doha, Eid H.; Ezz-Eldien, Samer S.; Abdelkawy, M. A.; Hafez, R. M.; Amin, A. Z. M.; Baleanu, Dumitru; Zaky, M. A.; 56389; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
This paper is devoted to investigate, from the numerical point of view, fractional-order Gegenbauer functions to solve fractional variational problems and fractional optimal control problems. We first introduce an orthonormal system of fractional-order Gegenbauer functions. Then, a formulation for the fractional-order Gegenbauer operational matrix of fractional integration is constructed. An error upper bound for the operational matrix of the fractional integration is also given. The properties of the fractional-order Gegenbauer functions are utilized to reduce the given optimization problems to systems of algebraic equations. Some numerical examples are included to demonstrate the efficiency and the accuracy of the proposed approach.
Citation Count: Jafari, H...et al. (2015). "A Decomposition Method for Solving Q-Difference Equations", Applied Mathematics and Information Sciences, Vol. 9, No. 6, pp. 2917-2920.
A Decomposition Method for Solving Q-Difference Equations
(Natural Sciences Publishing Corporation, 2015) Baleanu, Dumitru; Jafari, H.; Johnston, S. J.; Sani, S. M.; 56389; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
The q-difference equations are important in q-calculus. In this paper, we apply the iterative method which is suggested by Daftardar and Jafari, hereafter called the Daftardar-Jafari method, for solving a type of q-partial differential equations. We discuss the convergency of this method. In the implementation of this technique according to other iterative methods such as Adomian decomposition and homotopy perturbation methods, one does not need the calculation of the Adomian's polynomials for nonlinear terms. It is proven that under a special constraint, the given result by this method converges to exact solution of nonlinear q-ordinary or q-partial differential equations. © 2015 NSP Natural Sciences Publishing Cor.
Citation Count: Moradi, L.; Mohammadi, F.; Baleanu, D., "A direct numerical solution of time-delay fractional optimal control problems by using Chelyshkov wavelets", Journal of Vibration and Control, Vol. 25, No. 2, pp. 310-324, (2019).
A direct numerical solution of time-delay fractional optimal control problems by using Chelyshkov wavelets
(Sage Publications LTD, 2019-01) Moradi, L.; Mohammadi, F.; Baleanu, Dumitru; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
The aim of the present study is to present a numerical algorithm for solving time-delay fractional optimal control problems (TDFOCPs). First, a new orthonormal wavelet basis, called Chelyshkov wavelet, is constructed from a class of orthonormal polynomials. These wavelet functions and their properties are implemented to derive some operational matrices. Then, the fractional derivative of the state function in the dynamic constraint of TDFOCPs is approximated by means of the Chelyshkov wavelets. The operational matrix of fractional integration together with the dynamical constraints is used to approximate the control function directly as a function of the state function. Finally, these approximations were put in the performance index and necessary conditions for optimality transform the under consideration TDFOCPs into an algebraic system. Moreover, some illustrative examples are considered and the obtained numerical results were compared with those previously published in the literature.
Citation Count: Misra, S...et al. (2013). "A Discussion On the Role of People in Global Software Development [Rasprava O Ulozi Ljudi U Globalnom Razvoju Softvera]", Tehnicki Vjesnik, Vol. 20, No. 3, pp. 525-531.
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; 51704; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
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 Count: Ahmed, Idris...et al. "A Dynamical and Sensitivity Analysis of the Caputo Fractional-Order Ebola Virus Model: Implications for Control Measures", Science and Technology Asia, Science and Technology Asia, Vol. 28, No. 4, pp. 26-37.
A Dynamical and Sensitivity Analysis of the Caputo Fractional-Order Ebola Virus Model: Implications for Control Measures
(2023) Ahmed, Idris; Yusuf, Abdullahi; Tariboon, Jessada; Muhammad, Mubarak; Jarad, Fahd; Mikailu, Badamasi Bashir; 234808; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
The recurrence of outbreaks in cases of Ebola virus among African countries remains one of the greatest issues of concern. Practices such as hunting or consumption of contam-inated bush meat, unsafe funeral practices, and environmental contamination have all been implicated as possible contributors. This paper investigates the transmission dynamics of the Ebola virus model in the setting of a Caputo fractional-order derivative that accounts for both direct and indirect transmissions of the virus. By employing the concept of fixed theorems, we derived the existence and uniqueness results of the model. Moreover, we analyzed the forward normalized sensitivity indices to identify the critical parameters for controlling the infection and found that reducing the contact rate between infected individuals and susceptible vectors is vital to limiting the virus’s spread. Comparing the proposed fractional-order model with those of the previously developed integer-order model numerically, we found that the proposed model provides more reliable information on the model’s dynamics. Thus, we conclude that the Caputo fractional-order operator is a precise tool for describing the proposed model behavior and can help understand the complexities of Ebola virus disease outbreaks. © 2023, Thammasat University. All rights reserved.
Citation Count: Abdeljavad, T...et al. (2010). A fite type result for sequental fractional differintial equations. Dynamic System and Applications, 19(2), 383-394.
A fite type result for sequental fractional differintial equations
(Dynamic Publisher, 2010-06) Abdeljawad, Thabet; Baleanu, Dumitru; Jarad, Fahd; Mustafa, Octavian G.; Trujillo, J. J.; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü
Given the solution f of the sequential fractional differential equation aD(t)(alpha)(aD(t)(alpha) f) + P(t)f = 0, t is an element of [b, a], where -infinity < a < b < c < + infinity, alpha is an element of (1/2, 1) and P : [a, + infinity) -> [0, P(infinity)], P(infinity) < + infinity, is continuous. Assume that there exist t(1),t(2) is an element of [b, c] such that f(t(1)) = (aD(t)(alpha))(t(2)) = 0. Then, we establish here a positive lower bound for c - a which depends solely on alpha, P(infinity). Such a result might be useful in discussing disconjugate fractional differential equations and fractional interpolation, similarly to the case of (integer order) ordinary differential equations
Citation Count: Karapınar, Erdal; Öztürk, Ali; Rakocevic, Vladimir (2021). "A fixed point theorem for a system of Pachpatte operator equations", Aequationes Mathematicae, Vol. 95, No. 2, pp. 245-254.
A fixed point theorem for a system of Pachpatte operator equations
(2021-04) Karapınar, Erdal; Öztürk, Ali; Rakocevic, Vladimir; 19184; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
In this paper, we investigate sufficient conditions for the existence of solutions to the system {Tx=x, alpha(i)(x)=0(E), i = 1,2, ... r, where 0(E) is the zero vector of E, and alpha(i) : E -> E i = 1, 2, ... , r are mappings, T is a mapping satisfying the Pachpatte-contraction.
Citation Count: Karapınar, Erdal; Fulga, Andreea. (2023). "A fixed point theorem for Proinov mappings with a contractive iterate", Applied Mathematics-A Journal Of Chinese Universities Series B, Vol. 38, No. 3, pp. 403-412.
A fixed point theorem for Proinov mappings with a contractive iterate
(2023-09) Karapınar, Erdal; Fulga, Andreea; 19184; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
In this paper, we consider the fixed point theorem for Proinov mappings with a contractive iterate at a point. In other words, we combine and unify the basic approaches of Proinov and Sehgal in the framework of the complete metric spaces. We consider examples to illustrate the validity of the obtained result.
Citation Count: Arshad, Sadia...et al. (2018). "A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations", East Asian Journal on Applied Mathematics, Vol. 8, No. 4, pp. 764-781.
A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations
(Global Science Press, 2018-11) Arshad, Sadia; Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Zhao, Yue; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü
A finite difference method for a class of time-space fractional diffusion equations is considered. The trapezoidal formula and a fourth-order fractional compact difference scheme are, respectively, used in temporal and spatial discretisations and the method stability is studied. Theoretical estimates of the convergence in the L-2 -norm are shown to be O(tau(2) + h(4)), where tau and h are time and space mesh sizes. Numerical examples confirm theoretical results.
Citation Count: Baleanu, D...et al. (2016). A fractional derivative inclusion problem via an integral boundary condition. Journal of Computational Analysis and Applications, 21(3), 504-514.
A fractional derivative inclusion problem via an integral boundary condition
(Eudoxus Press, 2016-09) Baleanu, Dumitru; Moghaddam, Mehdi; Mohammadi, Hakimeh; Rezapour, Shahram; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü
We investigate the existence of solutions for the fractional differential inclusion (c)D(alpha)x(t) is an element of F(t, x(t)) (equipped with the boundary value problems x(0) = 0 and x(1) = integral(eta)(0) x(s)ds, where 0 < eta < 1, 1 < alpha <= 2, D-c(alpha) is the standard Caputo differentiation and F : [0, 1] x R -> 2(R) is a compact valued multifunction. An illustrative example is also discussed.
Citation Count: Salahshour, S...et al. "A fractional derivative with non-singular kernel for interval-valued functions under uncertainty", Optik, Vol. 130, pp. 273-286.
A fractional derivative with non-singular kernel for interval-valued functions under uncertainty
(Elsevier GMBH, 2017) Salahshour, S.; Ahmadian, Ali; İsmail, F.; Baleanu, Dumitru; 56389; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü
The purpose of the current investigation is to generalize the concept of fractional derivative in the sense of Caputo Fabrizio derivative (CF-derivative) for interval-valued function under uncertainty. The reason to choose this new approach is originated from the non singularity property of the kernel that is critical to interpret the memory aftermath of the system, which was not precisely illustrated in the previous definitions. We study the properties of CF-derivative for interval-valued functions under generalized Hukuhara-differentiability. Then, the fractional differential equations under this notion are presented in details. We also study three real-world systems such as the falling body problem, Basset and Decay problem under interval-valued CF-differentiability. Our cases involve a demonstration that this new notion is accurately applicable for the mechanical and viscoelastic models based on the interval CF-derivative equations.
Citation Count: Muslih, S.I., Agrawal, Om P., Baleanu, D. (2010). A fractional Dirac equation and its solution. Journal of Physics A-Mathematical and Theoretical, 43(5). http://dx.doi.org/10.1088/1751-8113/43/5/055203
A fractional Dirac equation and its solution
(IOP Publishing LTD, 2010-02-05) Muslih, Sami I.; Agrawal, Om. P.; Baleanu, Dumitru; Çankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümü
This paper presents a fractional Dirac equation and its solution. The fractional Dirac equation may be obtained using a fractional variational principle and a fractional Klein-Gordon equation; both methods are considered here. We extend the variational formulations for fractional discrete systems to fractional field systems defined in terms of Caputo derivatives. By applying the variational principle to a fractional action S, we obtain the fractional Euler-Lagrange equations of motion. We present a Lagrangian and a Hamiltonian for the fractional Dirac equation of order a. We also use a fractional Klein-Gordon equation to obtain the fractional Dirac equation which is the same as that obtained using the fractional variational principle. Eigensolutions of this equation are presented which follow the same approach as that for the solution of the standard Dirac equation. We also provide expressions for the path integral quantization for the fractional Dirac field which, in the limit a. 1, approaches to the path integral for the regular Dirac field. It is hoped that the fractional Dirac equation and the path integral quantization of the fractional field will allow further development of fractional relativistic quantum mechanics

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