Matematik Bölümü Yayın Koleksiyonu

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

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Citation - WoS: 24
Citation - Scopus: 25
Modified Modelling for Heat Like Equations Within Caputo Operator
(Mdpi, 2020) Khan, Adnan; Al-Qurashi, Maysaa; Shah, Rasool; Baleanu, Dumitru; Khan, Hassan
The present paper is related to the analytical solutions of some heat like equations, using a novel approach with Caputo operator. The work is carried out mainly with the use of an effective and straight procedure of the Iterative Laplace transform method. The proposed method provides the series form solution that has the desired rate of convergence towards the exact solution of the problems. It is observed that the suggested method provides closed-form solutions. The reliability of the method is confirmed with the help of some illustrative examples. The graphical representation has been made for both fractional and integer-order solutions. Numerical solutions that are in close contact with the exact solutions to the problems are investigated. Moreover, the sample implementation of the present method supports the importance of the method to solve other fractional-order problems in sciences and engineering.
Citation - WoS: 1
Citation - Scopus: 2
On the Complementary Nabla Pachpatte Type Dynamic Inequalities Via Convexity
(Elsevier, 2024) Kaymakcalan, Billur; Kayar, Zeynep
Pachpatte type inequalities are convex generalizations of the well-known Hardy-Copson type inequalities. As Hardy-Copson type inequalities and convexity have numerous applications in pure and applied mathematics, combining these concepts will lead to more significant applications that can be used to develop certain branches of mathematics such as fuctional analysis, operator theory, optimization and ordinary/partial differential equations. We extend classical nabla Pachpatte type dynamic inequalities by changing the interval of the exponent delta from delta > 1 to delta < 0. Our results not only complement the classical nabla Pachpatte type inequalities but also generalize complementary nabla Hardy-Copson type inequalities. As the case of delta < 0 has not been previously examined, these complementary inequalities represent a novelty in the nabla time scale calculus, specialized cases in continuous and discrete scenarios, and in the dual outcomes derived in the delta time scale calculus.
Numerical Analysis for the Effect of Irresponsible Immigrants on Hiv/Aids Dynamics
(Tech Science Press, 2023) Baleanu, Dumitru; Rafiq, Muhammad; Awrejcewicz, Jan; Ahmed, Nauman; Raza, Ali; Ahmad, Muhammad Ozair; Ali, Muhammad Tariq
The human immunodeficiency viruses are two species of Lentivirus that infect humans. Over time, they cause acquired immunodeficiency syndrome, a condition in which progressive immune system failure allows life-threatening opportunistic infections and cancers to thrive. Human immunodeficiency virus infection came from a type of chimpanzee in Central Africa. Studies show that immunodeficiency viruses may have jumped from chimpanzees to humans as far back as the late 1800s. Over decades, human immunodeficiency viruses slowly spread across Africa and later into other parts of the world. The Susceptible-Infected-Recovered (SIR) models are significant in studying disease dynamics. In this paper, we have studied the effect of irresponsible immigrants on HIV/AIDS dynamics by formulating and considering different methods. Euler, Runge Kutta, and a Non-standard finite difference (NSFD) method are developed for the same problem. Numerical experiments are performed at disease-free and endemic equilibria points at different time step sizes 'h'. The results reveal that, unlike Euler and Runge Kutta, which fail for large time step sizes, the proposed Non-standard finite difference (NSFD) method gives a convergence solution for any time step size. Our proposed numerical method is bounded, dynamically consistent, and preserves the positivity of the continuous solution, which are essential requirements when modeling a prevalent disease.
Citation - WoS: 11
Citation - Scopus: 15
Nimrad: Novel Technique for Respiratory Data Treatment
(Springer London Ltd, 2014) Nigmatullin, R. R.; Ionescu, C.; Baleanu, D.
This paper illustrates the efficiency and simplicity of a new technique which is determined in this paper as NIMRAD (the non-invasive methods of the reduced analysis of data) for describing information extracted from biological signals. As a specific example, we consider the respiratory data. The NIMRAD can be applied for quantitative description of data recorded for complex systems in cases where the adequate model is absent and the treatment procedure should not contain any uncontrollable error. The theoretical developments are applied to signals measured from the respiratory system by means of the forced oscillation technique based on non-invasive lung function test. In order to verify the feasibility of the proposed algorithm for developing new diagnosis tools, we apply NIMRAD on two different respiratory data sets, namely from a healthy subject and from a patient diagnosed with asthma. The results are promising and suggest that NIMRAD could be further tailored and used for specific clinical applications.
Citation - WoS: 21
Citation - Scopus: 28
Non-Instantaneous Impulsive Fractional Integro-Differential Equations With State-Dependent Delay Br
(Univ Maragheh, 2022) Salim, Abdelkrim; Aissani, Khalida; Benchohra, Mouffak; Karapinar, Erdal; Benkhettou, Nadia
This paper deals with the existence and uniqueness of the mild solution of the fractional integro-differential equations with non-instantaneous impulses and state-dependent delay. Our arguments are based on the fixed point theory. Finally, an example to confirm of the results is provided.
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
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.
Citation - Scopus: 1
A Uniqueness Result for Differential Pencils With Discontinuities From Interior Spectral Data
(De Gruyter, 2018) Baleanu, D.; Khalili, Y.
In this work, the interior spectral data is employed to study the inverse problem for a differential pencil with a discontinuity on the half line. By using a set of values of the eigenfunctions at some internal point and eigenvalues, we obtain the functions q0(x) and q1(x) applied in the diffusion operator. © 2018 Walter de Gruyter GmbH, Berlin/Boston.
Citation - WoS: 26
Citation - Scopus: 17
The First Integral Method for Wu-Zhang Nonlinear System With Time-Dependent Coefficients
(Editura Acad Romane, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Kilic, Bulent; Inc, Mustafa; Matematik
The first integral method is used to construct traveling wave solutions of Wu-Zhang nonlinear dynamical system with time-dependent coefficients. We obtained different types of exact solutions by using two types of variable transformations. The method is an effective tool to construct the different types.of exact solutions of nonlinear partial differential equations having real world applications.
Citation - WoS: 67
Citation - Scopus: 69
The Fractional Model of Spring Pendulum: New Features Within Different Kernels
(Editura Acad Romane, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; Matematik
In this work, new aspects of the fractional calculus (FC) are examined for a model of spring pendulum in fractional sense. First, we obtain the classical Lagrangian of the model, and as a result, we derive the classical Euler-Lagrange equations of the motion. Second, we generalize the classical Lagrangian to fractional case and derive the fractional Euler-Lagrange equations in terms of fractional derivatives with singular and nonsingular kernels, respectively. Finally, we provide the numerical solution of these equations within two fractional operators for some fractional orders and initial conditions. Numerical simulations verify that taking into account the recently features of the FC provides more realistic models demonstrating hidden aspects of the real-world phenomena.
Algebraic Integration of Sigma-Model Field Equations
(Springer, 2009) Yilmaz, N. T.
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: 12
Citation - Scopus: 14
Variational Principles in the Frame of Certain Generalized Fractional Derivatives
(Amer inst Mathematical Sciences-aims, 2020) Jarad, Fahd; Abdeljawad, Thabet
In this article, we study generalized fractional derivatives that contain kernels depending on a function on the space of absolute continuous functions. We generalize the Laplace transform in order to be applicable for the generalized fractional integrals and derivatives and apply this transform to solve some ordinary differential equations in the frame of the fractional derivatives under discussion.
Citation - WoS: 6
Citation - Scopus: 4
Discrete Variational Principles for Lagrangians Linear in Velocities
(Pergamon-elsevier Science Ltd, 2007) Jarad, Fahd; Baleanu, Dumitru
The discrete Hamiltonian formulation of Lagrangian linear in velocities is investigated and the equivalence of Hamilton and Euler-Lagrange equations is obtained. The role of Lagrange multipliers is discussed within discrete Lagrangian and Hamiltonian formulations for some systems with constraints. Three illustrative examples are investigated in details.
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
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: 100
Citation - Scopus: 117
A Fractional Model for the Dynamics of Tuberculosis Infection Using Caputo-Fabrizio Derivative
(Amer inst Mathematical Sciences-aims, 2020) Khan, Muhammad Altaf; Farooq, Muhammad; Hammouch, Zakia; Baleanu, Dumitru; Ullah, Saif
In the present paper, we study the dynamics of tuberculosis model using fractional order derivative in Caputo-Fabrizio sense. The number of confirmed notified cases reported by national TB program Khyber Pakhtunkhwa, Pakistan, from the year 2002 to 2017 are used for our analysis and estimation of the model biological parameters. The threshold quantity R-0 and equilibria of the model are determined. We prove the existence of the solution via fixed-point theory and further examine the uniqueness of the model variables. An iterative solution of the model is computed using fractional Adams-Bashforth technique. Finally, the numerical results are presented by using the estimated values of model parameters to justify the significance of the arbitrary fractional order derivative. The graphical results show that the fractional model of TB in Caputo-Fabrizio sense gives useful information about the complexity of the model and one can get reliable information about the model at any integer or non-integer case.
Citation - Scopus: 2
Quadruple Best Proximity Points With Applications To Functional and Integral Equations
(Wiley, 2022) Rashwan, Rashwan A.; Nafea, A.; Jarad, Fahd; Hammad, Hasanen A.
This manuscript is devoted to obtaining a quadruple best proximity point for a cyclic contraction mapping in the setting of ordinary metric spaces. The validity of the theoretical results is also discussed in uniformly convex Banach spaces. Furthermore, some examples are given to strengthen our study. Also, under suitable conditions, some quadruple fixed point results are presented. Finally, as applications, the existence and uniqueness of a solution to a system of functional and integral equations are obtained to promote our paper.
Citation - WoS: 6
Citation - Scopus: 4
Symmetries of the Dual Metrics
(World Scientific Publ Co Pte Ltd, 2002) Baleanu, D
In this paper the symmetries of the dual manifold are investigated. We found the conditions when the manifold and its dual admit the same Killing vectors and Killing-Yano tensors. The dual conformal Killing vectors and dual conformal Killing-Yano tensors were investigated. In the case of an Einstein's metric g(munu) the corresponding equations for its dual were found. The examples of Kerr-Newman geometry and the separable coordinates in 1 + 1 dimensions axe analyzed in details.
Citation - WoS: 2
Citation - Scopus: 3
An Extension of the Clark-Ocone Formula Under Benchmark Measure for Levy Processes
(Taylor & Francis Ltd, 2012) Okur, Yeliz Yolcu
The classical Clark-Ocone theorem states that any random variable F is an element of D-1,2(W) subset of L-2 (F-T, P) can be represented as F = E[F] + integral(T)(0) E[DtF vertical bar F-t]dWd(t), where E[.vertical bar F-t] denotes the conditional expectation, W(.) is a Brownian motion with canonical filtration {Ft}(t is an element of[0,T]) and D denotes the Malliavin derivative in the direction of W. Since many applications in financial mathematics require representation of random variables with respect to risk neutral martingale measure, an equivalent martingale measure version of this theorem was stated by Karatzas and Ocone (Stoch. Stoch. Rep. 34 (1991), 187-220). In this paper, we extend these results to be valid for square integrable pure jump Levy processes with no drift and for square integrable Ito-Levy processes using Malliavin calculus and white noise analysis. This extension might be useful for some applications in finance. As an application of our result, we calculate explicitly the closest hedge strategy for the digital option whose pay-off, F = chi([H,K))(S(T)) is not an element of D-1,2(W,(N) over tilde), is square integrable and the stock price S(.) is driven by a Levy process.
Citation - WoS: 6
Citation - Scopus: 5
Fixed Points of Generalized Contraction Mappings in Cone Metric Spaces
(Univ Osijek, dept Mathematics, 2011) Turkoglu, Duran; Abdeljawad, Thabet; Abuloha, Muhib; Abdeljawad, Thabet; Matematik
In this paper, we proved a fixed point theorem and a common fixed point theorem in cone metric spaces for generalized contraction mappings where some of the main results of Ciric in [8, 27] are recovered.
Citation - WoS: 2
Special Issue on Advances in Fractional Dynamics in Mechanical Engineering
(Sage Publications Ltd, 2016) Lopes, Antonio Mendes; Hristov, Jordan Yankov; Cattani, Carlo; Baleanu, Dumitru; Mohyud-Din, Syed Tauseef; Yang, Xiao-Jun
On the composition of the distributions x(+)(-r) and x(+)(mu)
(Indian Nat Sci Acad, 2005) Fisher, Brian; Taş, Kenan; Takaci, A.
Let F be a distirbution and let f be a locally summable function. The distribution F (f) is defined as the neutrix limit of the sequence {F-n(f)}, where F-n(x) = F(x) (*) delta(n)(x) and {delta(n)(x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta function delta(x). The distribution (x(+)(mu))(-r)(+) and (1 x 1(mu))(-r)(+) are evaluated for mu > 0, r = 1, 2,..., and k mu not equal 1, 2,....

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