Matematik Bölümü

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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 - 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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - 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.
Citation - Scopus: 8
Advanced Analysis of Local Fractional Calculus Applied To the Rice Theory in Fractal Fracture Mechanics
(Springer Science and Business Media Deutschland GmbH, 2022) Baleanu, D.; Srivastava, H.M.; Yang, X.-J.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this chapter, the recent results for the analysis of local fractional calculus are considered for the first time. The local fractional derivative (LFD) and the local fractional integral (LFI) in the fractional (real and complex) sets, the series and transforms involving the Mittag-Leffler function defined on Cantor sets are introduced and reviewed. The uniqueness of the solutions of the local fractional differential and integral equations and the local fractional inequalities are considered in detail. The local fractional vector calculus is applied to describe the Rice theory in fractal fracture mechanics. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
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 - 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: 10
Citation - Scopus: 10
Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set With Their Application To Solve Mcdm Problem
(Tech Science Press, 2023) Siddique, Imran; Ali, Rifaqat; Jarad, Fahd; Iampan, Aiyared; Zulqarnain, Rana Muhammad; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Experts use Pythagorean fuzzy hypersoft sets (PFHSS) in their investigations to resolve the indeterminate and imprecise information in the decision-making process. Aggregation operators (AOs) perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception. In this paper, we extend the concept of PFHSS to interval-valued PFHSS (IVPFHSS), which is the generalized form of interval -valued intuitionistic fuzzy soft set. The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set. It is the most potent method for amplifying fuzzy data in the decision-making (DM) practice. Some operational laws for IVPFHSS have been proposed. Based on offered operational laws, two inventive AOs have been established: interval-valued Pythagorean fuzzy hypersoft weighted average (IVPFHSWA) and interval-valued Pythagorean fuzzy hypersoft weighted geometric (IVPFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) shows an active part in contracts with the difficulties in industrial enterprise for material selection. But, the prevalent MCGDM approaches consistently carry irreconcilable consequences. Based on the anticipated AOs, a robust MCGDM technique is deliberate for material selection in industrial enterprises to accommodate this shortcoming. A real-world application of the projected MCGDM method for material selection (MS) of cryogenic storing vessels is presented. The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.
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.
Ample Spectrum Contractions in Branciari Distance Spaces
(Yokohama Publ, 2021) Karapinar, Erdal; Karapınar, Erdal; Lopez de Hierro, Antonio Francisco Roldan; Shahzad, Naseer; 19184; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 3
Citation - Scopus: 2
Analysis and Numerical Effects of Time-Delayed Rabies Epidemic Model With Diffusion
(Walter de Gruyter Gmbh, 2023) Rehman, Muhammad Aziz-Ur; Ahmed, Nauman; Baleanu, Dumitru; Iqbal, Muhammad Sajid; Rafiq, Muhammad; Raza, Ali; Jawaz, Muhammad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The current work is devoted to investigating the disease dynamics and numerical modeling for the delay diffusion infectious rabies model. To this end, a non-linear diffusive rabies model with delay count is considered. Parameters involved in the model are also described. Equilibrium points of the model are determined and their role in studying the disease dynamics is identified. The basic reproduction number is also studied. Before going towards the numerical technique, the definite existence of the solution is ensured with the help of the Schauder fixed point theorem. A standard result for the uniqueness of the solution is also established. Mapping properties and relative compactness of the operator are studied. The proposed finite difference method is introduced by applying the rules defined by R.E. Mickens. Stability analysis of the proposed method is done by implementing the Von-Neumann method. Taylor's expansion approach is enforced to examine the consistency of the said method. All the important facts of the proposed numerical device are investigated by presenting the appropriate numerical test example and computer simulations. The effect of tau on infected individuals is also examined, graphically. Moreover, a fruitful conclusion of the study is submitted.
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; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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: 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: 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: 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: 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: 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.

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