Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Citation - Scopus: 3
A close look at Newton–Cotes integration rules
(Cankaya University, 2019) Sermutlu, E.; Sermutlu, Emre; 17647; Matematik
Newton–Cotes integration rules are the simplest methods in numerical integration. The main advantage of using these rules in quadrature software is ease of programming. In practice, only the lower orders are implemented or tested, because of the negative coefficients of higher orders. Most textbooks state it is not necessary to go beyond Boole’s 5-point rule. Explicit coefficients and error terms for higher orders are seldom given literature. Higher-order rules include negative coefficients therefore roundoff error increases while truncation error decreases as we increase the number of points. But is the optimal one really Simpson or Boole? In this paper, we list coefficients up to 19-points for both open and closed rules, derive the error terms using an elementary and intuitive method, and test the rules on a battery of functions to find the optimum all-round one. © 2019, Cankaya University. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 4
A Decomposıtıon Algorıthm Coupled Wıth Operatıonal Matrıces Approach Wıth Applıcatıons To Fractıonal Dıfferentıal Equatıons
(Vinca inst Nuclear Sci, 2021) Talib, Imran; Baleanu, Dumitru; Alam, Md Nur; Baleanu, Dumitru; Zaidi, Danish; 56389; Matematik
In this article, we solve numerically the linear and non-linear fractional initial value problems of multiple orders by developing a numerical method that is based on the decomposition algorithm coupled with the operational matrices approach. By means of this, the fractional initial value problems of multiple orders are decomposed into a system of fractional initial value problems which are then solved by using the operational matrices approach. The efficiency and advantage of the developed numerical method are highlighted by comparing the results obtained otherwise in the literature. The construction of the new derivative operational matrix of fractional legendre function vectors in the Caputo sense is also a part of this research. As applications, we solve several fractional initial value problems of multiple orders. The numerical results are displayed in tables and plots.
Citation - Scopus: 15
A Decomposition Method for Solving Q-Difference Equations
(Natural Sciences Publishing Co., 2015) Jafari, H.; Baleanu, Dumitru; Johnston, S.J.; Sani, S.M.; Baleanu, D.; 56389; Matematik
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 - WoS: 5
Citation - Scopus: 6
A discussion on a pata type contraction via iterate at a point
(Univ Nis, Fac Sci Math, 2020) Karapinar, Erdal; Karapınar, Erdal; Fulga, Andreea; Rakocevic, Vladimir; 19184; Matematik
In this paper, we introduce the notion of Pata type contraction at a point in the context of a complete metric space. We observe that such contractions possesses unique fixed point without continuity assumption on the given mapping. Thus, is extended the original results of Pata. We also provide an example to illustrate its validity.
Citation - WoS: 2
Citation - Scopus: 2
A discussion on the coincidence quasi-best proximity points
(Univ Nis, Fac Sci Math, 2021) Fouladi, Farhad; Karapınar, Erdal; Abkar, Ali; Karapinar, Erdal; 19184; Matematik
In this paper, we first introduce a new class of the pointwise cyclic-noncyclic proximal contraction pairs. Then we consider the coincidence quasi-best proximity point problem for this class. Finally, we study the coincidence quasi-best proximity points of weak cyclic-noncyclic Kannan contraction pairs. We consider an example to indicate the validity of the main result.
Citation - WoS: 22
Citation - Scopus: 22
A discussion on the role of people in global software development
(Univ Osijek, Tech Fac, 2013) Misra, Sanjay; Colomo-Palacios, Ricardo; Pusatli, Tolga; Soto-Acosta, Pedro; 51704
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: 2
Citation - Scopus: 3
A Drone-Based Blood Donation Approach Using an Ant Colony Optimization Algorithm
(Tech Science Press, 2023) Abbas, Sana; Jarad, Fahd; Ashraf, Faraha; Jarad, Fahd; Sardar, Muhammad Shoaib; Siddique, Imran; 234808; Matematik
This article presents an optimized approach of mathematical techniques in the medical domain by manoeuvring the phenomenon of ant colony optimization algorithm (also known as ACO). A complete graph of blood banks and a path that covers all the blood banks without repeating any link is required by applying the Travelling Salesman Problem (often TSP). The wide use promises to accelerate and offers the opportunity to cultivate health care, particularly in remote or unmerited environments by shrinking lab testing reversal times, empowering just-in-time lifesaving medical supply.
Citation - WoS: 0
Citation - Scopus: 1
A Fixed Point Theorem and an Application for the Cauchy Problem in the Scale of Banach Spaces
(Univ Nis, Fac Sci Math, 2020) Vo Viet Tri; Karapınar, Erdal; Karapinar, Erdal; 19184; Matematik
The main aim of this paper is to prove the existence of the fixed point of the sum of two operators in setting of the cone-normed spaces with the values of cone-norm belonging to an ordered locally convex space. We apply this result to prove the existence of global solution of the Cauchy problem with perturbation of the form {x'(t) = f[t, x(t)] + g[t, x(t)], t is an element of[0,infinity), x(0) = x(0)is an element of F-1, in a scale of Banach spaces f(F-s; parallel to center dot parallel to(s)) : s is an element of(0, 1]}.
Citation - WoS: 1
Citation - Scopus: 2
A fixed point theorem for a system of Pachpatte operator equations
(Springer Basel Ag, 2021) Karapinar, Erdal; Karapınar, Erdal; Ozturk, Ali; Rakocevic, Vladimir; 19184; Matematik
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 - WoS: 4
Citation - Scopus: 2
A fixed point theorem for Proinov mappings with a contractive iterate
(Zhejiang Univ Press, 2023) Karapinar, Erdal; Karapınar, Erdal; Fulga, Andreea; 19184; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik Bölümü; Matematik
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 - WoS: 2
Citation - Scopus: 1
A fixed point theorem on multiplicative metric space with integral-type inequality
(Journal Mathematics & Computer Science-jmcs, 2018) Khan, Aziz; Baleanu, Dumitru; Khan, Hasib; Baleanu, Dumitru; Jafari, Hossein; Khan, Tahir Saeed; Alqurashi, Maysaa; 56389; Matematik
In this paper, we prove fixed point theorems (FPTs) on multiplicative metric space (MMS) (X, triangle) by the help of integral-type contractions of self-quadruple mappings (SQMs), i.e., for p(1), p(2), p(3), p(4) : X -> R. For this, we assume that the SQMs are weakly compatible mappings and the pairs (p(1), p(3)) and (p(2), p(4)) satisfy the property (CLRp3p4). Further, two corollaries are produced from our main theorem as special cases. The novelty of these results is that for the unique common fixed point (CFP) of the SQMs p(1), p(2), p(3), p(4), we do not need to the assumption of completeness of the MMS (X, triangle). These results generalize the work of Abdou, [A. A. N. Abdou, J. Nonlinear Sci. Appl., 9 (2016), 2244-2257], and many others in the available literature.
Citation - Scopus: 3
A fixed point theorem without a Picard operator
(Cankaya University, 2021) Karapınar, E.; Karapınar, Erdal; 19184; Matematik
In this short note, we propose a fixed point theorem in the setting of a Banach space without using a Picard operator. © 2021, Cankaya University. All rights reserved.
Citation - WoS: 5
Citation - Scopus: 7
A FRACTIONAL STUDY OF MHD CASSON FLUID MOTION WITH THERMAL RADIATIVE FLUX AND HEAT INJECTION/SUCTION MECHANISM UNDER RAMPED WALL CONDITION: APPLICATION OF RABOTNOV EXPONENTIAL KERNEL
(Sciendo, 2024) Rehman, Aziz Ur; Jarad, Fahd; Jarad, Fahd; Riaz, Muhammad Bilal; 234808; Matematik
The primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of magnetohydrodynamic (MHD) natural convective flow of Casson fluid is conducted, focusing on obtaining analytical solutions using the non-integer-order derivative known as the Yang-Abdel-Aty-Cattani (YAC) operator. The YAC operator utilized in this research possesses a more generalized exponential kernel. The fluid flow is examined in the vicinity of an infinitely vertical plate with a characteristic velocity denoted as u(0). The mathematical modelling of the problem incorporates partial differential equations, incorporating Newtonian heating and ramped conditions. To facilitate the analysis, a suitable set of variables is introduced to transform the governing equations into a dimensionless form. The Laplace transform (LT) is then applied to the fractional system of equations, and the obtained results are presented in series form and also expressed in terms of special functions. The study further investigates the influence of relevant parameters, such as alpha, beta, P-r, Q, Gr, M, N-r and K, on the fluid flow to reveal interesting findings. A comparison of different approaches reveals that the YAC method yields superior results compared to existing operators found in the literature. Graphs are generated to illustrate the outcomes effectively. Additionally, the research explores the limiting cases of the Casson and viscous fluid models to derive the classical form from the YAC fractionalized Casson fluid model.
Citation - WoS: 15
Citation - Scopus: 17
A Fractional Variational Approach to the Fractional Basset-Type Equation
(Pergamon-elsevier Science Ltd, 2013) Baleanu, Dumitru; Baleanu, Dumitru; Garra, Roberto; Petras, Ivo; 56389; Matematik
In this paper we discuss an application of fractional variational calculus to the Basset-type fractional equations. It is well known that the unsteady motion of a sphere immersed in a Stokes fluid is described by an integro-differential equation involving derivative of real order. Here we study the inverse problem, i.e. we consider the problem from a Lagrangian point of view in the framework of fractional variational calculus. In this way we find an application of fractional variational methods to a classical physical model, finding a Basset-type fractional equation starting from a Lagrangian depending on derivatives of fractional order.
Citation - WoS: 13
Citation - Scopus: 14
A generalisation of the Malgrange-Ehrenpreis theorem to find fundamental solutions to fractional PDEs
(Univ Szeged, Bolyai institute, 2017) Baleanu, Dumitru; Baleanu, Dumitru; Fernandez, Arran; 56389; Matematik
We present and prove a new generalisation of the Malgrange-Ehrenpreis theorem to fractional partial differential equations, which can be used to construct fundamental solutions to all partial differential operators of rational order and many of arbitrary real order. We demonstrate with some examples and mention a few possible applications.
Citation - WoS: 17
Citation - Scopus: 20
A high-order unconditionally stable numerical method for a class of multi-term time-fractional diffusion equation arising in the solute transport models
(Taylor & Francis Ltd, 2023) Alam, Mohammad Prawesh; Baleanu, Dumitru; Khan, Arshad; Baleanu, Dumitru; 56389; Matematik
In this paper, we study a high-order unconditionally stable numerical method to approximate the class of multi-term time-fractional diffusion equations. This type of problem appears in the modelling of transport of certain quantities such as heat, mass, energy, solutes in ground water and soils. The multi-term time-fractional derivative is approximated by using the Crank-Nicolson method for the Caputo's time derivative. The space derivative is approximated by using the collocation method based on quintic B-spline basis functions. We have established the stability and convergence analysis of the proposed numerical scheme thoroughly, and it is shown that the order of convergence in space variable is almost four and in the time variable is O (Delta t(2-max{gamma,gamma i})). To prove the accuracy and efficiency of the developed method, we consider four numerical examples and perform the numerical simulation. The developed algorithm works well andvalidate the theoretical results. The developed method is fourth-order convergent in the space variable, which is almost two orders of magnitude higher than the other spline collocation methods.
Citation - WoS: 36
A lie group approach to solve the fractional poisson equation
(Editura Acad Romane, 2015) Hashemi, M. S.; Baleanu, Dumitru; Baleanu, D.; Parto-Haghighi, M.; Matematik
In the present paper, approximate solutions of fractional Poisson equation (FPE) have been considered using an integrator in the class of Lie groups, namely, the fictitious time integration method (FTIM). Based on the FTIM, the unknown dependent variable u(x, t) is transformed into a new variable with one more dimension. We use a fictitious time tau as the additional dimension (fictitious dimension), by transformation: v(x, t, tau) := (1 + tau)(k) u(x, t), where 0 < k <= 1 is a parameter to control the rate of convergency in the FTIM. Then the group preserving scheme (GPS) is used to integrate the new fractional partial differential equations in the augmented space R2+1. The power and the validity of the method are demonstrated using two examples.
Citation - WoS: 54
Citation - Scopus: 81
A Modification Fractional Variational Iteration Method For Solving Non-Linear Gas Dynamic and Coupled Kdv Equations Involving Local Fractional Operators
(Vinca inst Nuclear Sci, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Jassim, Hassan Kamil; Khan, Hasib; 56389; Matematik
In this paper, we apply a new technique, namely local fractional variational iteration transform method on homogeneous/non-homogeneous non-linear gas dynamic and coupled KdV equations to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative and integral operators. This method is the combination of the local fractional Laplace transform and variational iteration method. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
Citation - WoS: 19
Citation - Scopus: 18
A new application of chemometric techniques to HPLC data for the simultaneous analysis of a two-component mixture
(Taylor & Francis inc, 2005) Dinç, E; Baleanu, Dumitru; Üstündag, Ö; Özdemir, A; Baleanu, D; 56389; Matematik
A new chemometric approach using high performance liquid chromatography (HPLC) with photodiode array (PDA) detection was developed and applied to the simultaneous determination of enalapril maleate (EA) and hydrochlorothiazide (HCT) in tablets. Chernometric calibration techniques, classical least squares (CLS), principle component regression (PCR), and partial least squares (PLS) were subjected to the peak area at multiwavelength PDA detector responses. The combination of HPLC and chernometric calibration techniques was called HPLC-CLS, HPLC-PCR, and HPLC-PLS. For comparison purposes, the HPLC method called classical HPLC method was used for the confirmation of the results obtained from combined HPLC-chemometric calibration techniques. A good chromatographic separation between two drugs and internal standard (IS) was achieved using a Waters Symmetry (R) C 18 Column 5 mu m 4.6 x 250 mm and a mobile phase consisting of 0.2M acetate buffer and acetonitrile (v/v, 60:40). The multiwavelength PDA detection was done at 230 (A), 240 (B), 250 (C), 250 (D), 240 (E) nm wavelengths, and peak area was recorded for the concentration set in the mobile phase. Three HPLC-chemometric calibrations and a classical-HPLC method were tested by analyzing the synthetic mixture of EA and HCT in the presence of losartan potassium (IS). The proposed methods were applied to real samples containing the present two drugs. The obtained results were statistically compared with each other.
Citation - WoS: 35
Citation - Scopus: 37
A New Application of the Fractional Logistic Map
(Editura Acad Romane, 2016) Huang, Lan-Lan; Baleanu, Dumitru; Baleanu, Dumitru; Wu, Guo-Cheng; Zeng, Sheng-Da; 56389; Matematik
The fractional chaotic map started to be applied in physics and engineering to properly treat some real-world phenomena. A shuffling method is proposed based on the fractional logistic map. The fractional difference order is used as a key. An image encryption scheme is designed by using the XOR operation and the security analysis is given. The obtained results demonstrate that the fractional difference order makes the encryption scheme highly secure.

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