Matematik Bölümü

Permanent URI for this communityhttps://hdl.handle.net/20.500.12416/412

Browse

Now showing 1 - 20 of 304

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: 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: 4
Citation - Scopus: 4
A Fourth Order Finite Difference Method for Time-Space Fractional Diffusion Equations
(Global Science Press, 2018) Arshad, Sadia; Baleanu, Dumitru; Baleanu, Dumitru; Huang, Jianfei; Tang, Yifa; Zhao, Yue; 56389; Matematik
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 - WoS: 66
Citation - Scopus: 77
A fractional schrödinger equation and its solution
(Springer/plenum Publishers, 2010) Muslih, Sami I.; Baleanu, Dumitru; Agrawal, Om P.; Baleanu, Dumitru; Matematik
This paper presents a fractional Schrodinger equation and its solution. The fractional Schrodinger 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 to obtain the fractional Euler-Lagrange equations of motion. We present the Lagrangian for the fractional Schrodinger equation of order alpha. We also use a fractional Klein-Gordon equation to obtain the fractional Schrodinger equation which is the same as that obtained using the fractional variational principle. As an example, we consider the eigensolutions of a particle in an infinite potential well. The solutions are obtained in terms of the sines of the Mittag-Leffler function.
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: 4
Citation - Scopus: 5
A Mechanical Model Based on Conformal Strain Energy and Its Application to Bending and Buckling of Nanobeam Structures
(Asme, 2019) Rahimi, Zaher; Baleanu, Dumitru; Sumelka, Wojciech; Baleanu, Dumitru; 56389; Matematik
In the present work, a nonlocal model based on the conformal strain energy, utilizing the conformable derivative definition, has been obtained. The model has two additional free parameters compared to the classical (local) mechanical formulations. The first one specifies the amount of the integer and the noninteger gradient of strain in the strain energy relation, and the second one controls the order of the strain derivatives in the conformable energy relation. The obtained governing (nonlinear) equation has been solved by the Galerkin method and the effects of both free parameters have been shown. As a case study, the bending and buckling of nanobeam structures has been studied.
Citation - WoS: 107
Citation - Scopus: 118
A New Analysis of Fractional Fish Farm Model Associated With Mittag-Leffler-Type Kernel
(World Scientific Publ Co Pte Ltd, 2020) Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra; Baleanu, Dumitru; 56389; Matematik
In this paper, we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order. The model is constituted with the group of non-linear differential equations having nutrients, fish and mussel. We have included discrete kind gestational delay of fish. The solution of fish farm model is determined by employing homotopy analysis transforms method (HATM). Existence of and uniqueness of solution are studied through Picard-Lindelof approach. The influence of order of new non-integer order derivative on nutrients, fish and mussel is discussed. The complete study reveals that the outer food supplies manage the behavior of the model. Moreover, to show the outcomes of the study, some numerical results are demonstrated through graphs.
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.
Citation - WoS: 5
A new existence results on fractional differential inclusions with state-dependent delay and Mittag-Leffler kernel in Banach space
(Ovidius Univ Press, 2022) Arjunan, Mani Mallika; Baleanu, Dumitru; Kavitha, Velusamy; Baleanu, Dumitru; 56389; Matematik
In this manuscript the existence of the fractional-order functional differential inclusions [FFDI] with state-dependent delay [SDD] is investigated within the Mittag-Leffler kernel. We use both contractive and condensing maps to prove the existence of mild solutions through solution operator. Finally, an example is presented to illustrate the theoretical findings.
Citation - WoS: 20
Citation - Scopus: 22
A new extension of hesitant fuzzy set: An application to an offshore wind turbine technology selection process
(inst Engineering Technology-iet, 2021) Narayanamoorthy, Samayan; Baleanu, Dumitru; Ramya, Lakshmanaraj; Kang, Daekook; Baleanu, Dumitru; Kureethara, Joseph Varghese; Annapoorani, Veerappan; 56389; Matematik
Wind energy is an energy source that is naturally clean, safe and cheap. It comes from a variety of sources. The electric energy generated by a wind turbine manifests as kinetic energy throughout the earth. The energy received from the wind is clean and is permanently available and can be generated forever. Turbine characteristics also have an impact on wind energy production. The turbine properties within a wind farm are important in estimating the load on power generation and wind turbine energy. The amount of energy released is calculated according to the type of the turbine model applied. In many situations, the choices of turbine model can incur various vague and complicated hesitation situations. To manage this situation, a hesitant fuzzy set with the Multi Criteria Decision Making (MCDM) is used. In the present research, the newly proposed Normal Wiggly Hesitant Fuzzy-Criteria Importance Through Intercriteria Correlation (NWHF-CRITIC) and Normal Wiggly Hesitant Fuzzy-Multi Attribute Utility Theory (NWHF-MAUT) methods were employed to rank turbine models based on quality, power level, voltage, and capacity. As part of this process, the NWHF method was utilized to extract and gather deeper information from the decision-makers.
Citation - WoS: 37
A new fractional derivative for differential equation of fractional order under interval uncertainty
(Sage Publications Ltd, 2015) Salahshour, Soheil; Baleanu, Dumitru; Ahmadian, Ali; Ismail, Fudzial; Baleanu, Dumitru; Senu, Norazak; Matematik
In this article, we develop a new definition of fractional derivative under interval uncertainty. This fractional derivative, which is called conformable fractional derivative, inherits some interesting properties from the integer differentiability which is more convenient to work with the mathematical models of the real-world phenomena. The interest for this new approach was born from the notion that makes a dependency just on the basic limit definition of the derivative. We will introduce and prove the main features of this well-behaved simple fractional derivative under interval arithmetic uncertainty. The actualization and usefulness of this approach are validated by solving two practical models.
Citation - WoS: 59
Citation - Scopus: 62
A New Generalized Laguerre-Gauss Collocation Scheme For Numerical Solution Of Generalized Fractional Pantograph Equations
(Editura Acad Romane, 2014) Bhrawy, A. H.; Baleanu, Dumitru; Al-Zahrani, A. A.; Alhamed, Y. A.; Baleanu, D.; 56389; Matematik
The manuscript is concerned with a generalization of the fractional pantograph equation which contains a linear functional argument. This type of equation has applications in many branches of physics and engineering. A new spectral collocation scheme is investigated to obtain a numerical solution of this equation with variable coefficients on a semi-infinite domain. This method is based upon the generalized Laguerre polynomials and Gauss quadrature integration. This scheme reduces solving the generalized fractional pantograph equation to a system of algebraic equations. Numerical results indicating the high accuracy and effectiveness of this algorithm are presented.
Citation - WoS: 2
Citation - Scopus: 2
A new insight to the Hamiltonian systems with a finite number of spectral parameters
(Taylor & Francis Ltd, 2023) Ugurlu, Ekin; Uğurlu, Ekin; 238990; Matematik
In this article, we introduce a new first-order differential equation containing a finite number of spectral parameters and some results on the solutions of this equation. In particular, with the aid of the nested-circles approach we share a lower bound for the number of linearly independent square-integrable solutions of the equation. We share some limit-point criterias. Moreover, we show that some known and unknown scalar and matrix differential equations can be embedded into this new first-order equation. Using the obtained results we present some additional results for some system of scalar multiparameter differential equations. Finally, we share some relations between the characteristic function of a regular boundary-value problem and the kernel of related integral operator.
Citation - WoS: 27
Citation - Scopus: 32
A new iterative algorithm on the time-fractional Fisher equation: Residual power series method
(Sage Publications Ltd, 2017) Al Qurashi, Maysaa' Mohamed; Baleanu, Dumitru; Korpinar, Zeliha; Baleanu, Dumitru; Inc, Mustafa; 56389; Matematik
In this article, the residual power series method is used to solve time-fractional Fisher equation. The residual power series method gets Maclaurin expansion of the solution. The solutions of present equation are computed in the shape of quickly convergent series with quickly calculable fundamentals using mathematica software package. Explanation of the method is given by graphical consequences and series solutions are made use of to represent our solution. The found consequences show that technique is a power and efficient method in conviction of solution time-fractional Fisher equation.
Citation - WoS: 13
Citation - Scopus: 19
A New Medical Image Enhancement Algorithm Based on Fractional Calculus
(Tech Science Press, 2021) Jalab, Hamid A.; Baleanu, Dumitru; Ibrahim, Rabha W.; Hasan, Ali M.; Karim, Faten Khalid; Al-Shamasneh, Ala'a R.; Baleanu, Dumitru; 56389; Matematik
The enhancement of medical images is a challenging research task due to the unforeseeable variation in the quality of the captured images. The captured images may present with low contrast and low visibility, which might influence the accuracy of the diagnosis process. To overcome this problem, this paper presents a new fractional integral entropy (FITE) that estimates the unforeseeable probabilities of image pixels, posing as the main contribution of the paper. The proposed model dynamically enhances the image based on the image contents. The main advantage of FITE lies in its capability to enhance the low contrast intensities through pixels? probability. Initially, the pixel probability of the fractional power is utilized to extract the illumination value from the pixels of the image. Next, the contrast of the image is then adjusted to enhance the regions with low visibility. Finally, the fractional integral entropy approach is implemented to enhance the low visibility contents from the input image. Tests were conducted on brain MRI, lungs CT, and kidney MRI scans datasets of different image qualities to show that the proposed model is robust and can withstand dramatic variations in quality. The obtained comparative results show that the proposed image enhancement model achieves the best BRISQUE and NIQE scores. Overall, this model improves the details of brain MRI, lungs CT, and kidney MRI scans, and could therefore potentially help the medical staff during the diagnosis process.
Citation - WoS: 2
Citation - Scopus: 30
A new method for approximate solutions of some nonlinear equations: Residual power series method
(Sage Publications Ltd, 2016) Inc, Mustafa; Baleanu, Dumitru; Korpinar, Zeliha S.; Al Qurashi, Maysaa' Mohamed; Baleanu, Dumitru; Matematik
In this work, a powerful iterative method called residual power series method is introduced to obtain approximate solutions of nonlinear time-dependent generalized Fitzhugh-Nagumo equation with time-dependent coefficients and Sharma-Tasso-Olver equation subjected to certain initial conditions. The consequences show that this method is efficient and convenient, and can be applied to a large sort of problems. The approximate solutions are compared with the known exact solutions.
Citation - WoS: 8
Citation - Scopus: 8
A new method for dissipative dynamic operator with transmission conditions
(Springer Basel Ag, 2018) Uğurlu, Ekin; Ugurlu, Ekin; Tas, Kenan; Taş, Kenan; 238990; 4971; Matematik
In this paper, we investigate the spectral properties of a boundary value transmission problem generated by a dynamic equation on the union of two time scales. For such an analysis we assign a suitable dynamic operator which is in limit-circle case at infinity. We also show that this operator is a simple maximal dissipative operator. Constructing the inverse operator we obtain some information about the spectrum of the dissipative operator. Moreover, using the Cayley transform of the dissipative operator we pass to the contractive operator which is of the class With the aid of the minimal function we obtain more information on the dissipative operator. Finally, we investigate other properties of the contraction such that multiplicity of the contraction, unitary colligation with basic operator and CMV matrix representation associated with the contraction.

Browse

Browsing Matematik Bölümü by WoS Q "Q3"