Matematik Bölümü Yayın Koleksiyonu

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

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Citation - WoS: 5
Exact Solutions of the Laplace Fractional Boundary Value Problems Via Natural Decomposition Method
(de Gruyter Poland Sp Z O O, 2020) Khan, Hassan; Chu, Yu-Ming; Shah, Rasool; Baleanu, Dumitru; Arif, Muhammad; Hajira
In this article, exact solutions of some Laplace-type fractional boundary value problems (FBVPs) are investigated via natural decomposition method. The fractional derivatives are described within Caputo operator. The natural decomposition technique is applied for the first time to boundary value problems (BVPs) and found to be an excellent tool to solve the suggested problems. The graphical representation of the exact and derived results is presented to show the reliability of the suggested technique. The present study is mainly concerned with the approximate analytical solutions of some FBVPs. Moreover, the solution graphs have shown that the actual and approximate solutions are very closed to each other. The comparison of the proposed and variational iteration methods is done for integer-order problems. The comparison, support strong relationship between the results of the suggested techniques. The overall analysis and the results obtained have confirmed the effectiveness and the simple procedure of natural decomposition technique for obtaining the solution of BVPs.
Citation - WoS: 86
Citation - Scopus: 82
On Nonautonomous Complex Wave Solutions Described by the Coupled Schrodinger-Boussinesq Equation With Variable-Coefficients
(Springer, 2018) Machado, J. A. T.; Baleanu, Dumitru; Osman, M. S.
This paper investigates the coupled Schrodinger-Boussinesq equation with variable-coefficients using the unified method. New nonautonomous complex wave solutions are obtained and classified into two categories, namely polynomial function and rational function solutions. For the polynomial functions emerge the complex solitary, complex soliton and complex elliptic wave solutions, while for the rational function are observed complex periodic rational and complex hyperbolic rational wave solutions. The physical insight and the dynamical behavior of the solutions describing the wave propagation in laser or plasma physics are discussed and analysed for different choices of the arbitrary functions in the solutions.
Optical solitons to the (n+1)-dimensional nonlinear Schrodinger's equation with Kerr law and power law nonlinearities using two integration schemes
(2019) İnç, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Bayram, Mustafa; Baleanu, Dumitru
In this study, two integration techniques are employed to reach optical solitons to the (n + 1)-dimensional nonlinear Schrodinger's equation ((n + 1)-NLSE) with Kerr and power laws nonlinearities. These are the undetermined coefficient and Bernoulli sub-ODE methods. We acquired bright, dark, and periodic singular soliton solutions. The necessary conditions for the existence of these solitons are presented.
Citation - WoS: 87
Citation - Scopus: 96
On Electromagnetic Field in Fractional Space
(Pergamon-elsevier Science Ltd, 2010) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Baleanu, Dumitru
Laplacian equation in fractional space describes complex phenomena of physics. With this view, potential of charge distribution in fractional space is derived using Gegenbauer polynomials. Multipoles and magnetic field of charges in fractional space have been obtained. (C) 2008 Elsevier Ltd. All rights reserved.
Citation - WoS: 51
Citation - Scopus: 60
Lie Symmetry Analysis and Explicit Solutions for the Time Fractional Generalized Burgers-Huxley Equation
(Springer, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
In this work, we study the time fractional generalized Burgers-Huxley equation with Riemann-Liouville derivative via Lie symmetry analysis and power series expansion method. We transform the governing equation to nonlinear ordinary differential equation of fractional order using its Lie point symmetries. In the reduced equation, the derivative is in Erdelyi-Kober sense. We apply power series technique to derive explicit solutions for the reduced equation. The convergence of the obtained power series solutions are also derived. Some interesting Figures for the obtained solutions are presented.
From Eikonal To Antieikonal Approximations: Competition of Scales in the Framework of Schrodinger and Classical Wave Equation
(Asme, 2022) Pilar Velasco, M.; Baleanu, Dumitru; Luis Vazquez-Poletti, J.; Jimenez, Salvador; Vazquez, Luis
We present a description of certain limits associated with the Schrodinger equation, the classical wave equation, and Maxwell equations. Such limits are mainly characterized by the competition of two fundamental scales. More precisely: (1) The competition of an exploratory wavelength and the scale of fluctuations is associated with the media where the propagation takes place. From that, the universal behaviors arise eikonal and anti-eikonal. (2) In the context above, it is specially relevant and promising the study of propagation of electromagnetic waves in a media with a self-similar structure, like a fractal one. These systems offer the suggestive scenario where the eikonal and anti-eikonal behaviors are simultaneous. This kind of study requires large and massive computations that are mainly possible in the framework of the cloud computing. Recently, we started to carry out this task. (3) Finally and as a collateral aspect, we analyze the Planck constant in the interval 0 <= h <= infinity.
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: 49
Citation - Scopus: 56
An Efficient Numerical Technique for the Nonlinear Fractional Kolmogorov-Petrovskii Equation
(Mdpi, 2019) Prakasha, Doddabhadrappla Gowda; Baleanu, Dumitru; Veeresha, Pundikala
The q-homotopy analysis transform method (q-HATM) is employed to find the solution for the fractional Kolmogorov-Petrovskii-Piskunov (FKPP) equation in the present frame work. To ensure the applicability and efficiency of the proposed algorithm, we consider three distinct initial conditions with two of them having Jacobi elliptic functions. The numerical simulations have been conducted to verify that the proposed scheme is reliable and accurate. Moreover, the uniqueness and convergence analysis for the projected problem is also presented. The obtained results elucidate that the proposed technique is easy to implement and very effective to analyze the complex problems arising in science and technology.
Citation - WoS: 142
Citation - Scopus: 161
On the Existence of Solutions for Some Infinite Coefficient-Symmetric Caputo-Fabrizio Fractional Integro-Differential Equations
(Springeropen, 2017) Mousalou, Asef; Rezapour, Shahram; Baleanu, Dumitru
By mixing the idea of 2-arrays, continued fractions, and Caputo-Fabrizio fractional derivative, we introduce a new operator entitled the infinite coefficient-symmetric Caputo-Fabrizio fractional derivative. We investigate the approximate solutions for two infinite coefficient-symmetric Caputo-Fabrizio fractional integro-differential problems. Finally, we analyze two examples to confirm our main results.
Citation - WoS: 2
Citation - Scopus: 2
On Wong Type Contractions
(Mdpi, 2020) Fulga, Andreea; Karapinar, Erdal
In this paper, by using admissible mapping, Wong type contraction mappings are extended and investigated in the framework of quasi-metric spaces to guarantee the existence of fixed points. We consider examples to illustrate the main results. We also demonstrate that the main results of the paper cover several existing results in the literature.
Citation - WoS: 9
Citation - Scopus: 9
Positivity Preserving Computational Techniques for Nonlinear Autocatalytic Chemical Reaction Model
(Editura Acad Romane, 2020) Ahmed, Nauman; Baleanu, Dumitru; Baleanu, Dumitru; Korkmaz, Alper; Rafiq, Muhammad; Rehman, Muhammad Aziz-Ur; Ali, Mubasher; Matematik
In many physical problems, positivity is one of the most prevalent and imperative attribute of diverse mathematical models such as concentration of chemical reactions, population dynamics etc. However, the numerical discretization of dynamical systems that illustrate negative values may lead to meaningless solutions and sometimes to their divergence. The main objective of this work is to develop positivity preserving numerical schemes for the two-dimensional autocatalytic reaction diffusion Brusselator model. Two explicit finite difference (FD) schemes are proposed to solve numerically the two-dimensional Brusselator system. The proposed methods are the non-standard finite difference (NSFD) scheme and the unconditionally positivity preserving scheme. These numerical methods retain the positivity of the solution and the stability of the equilibrium point. Both proposed numerical schemes are compared with the forward Euler explicit FD scheme. The stability and consistency of all schemes are proved analytically and then verified by numerical simulations.
Novel precise solutions and bifurcation of traveling wave solutions for the nonlinear fractional (3 + 1) -dimensional WBBM equation
(2023) Siddique, Imran; Mehdi, Khush Bukht; Jarad, Fahd; Elbrolosy, Mamdouh E.; Elmandouh, Adel A.
The nonlinear fractional differential equations (FDEs) are composed by mathematical modeling through nonlinear corporeal structures. The study of these kinds of models has an energetic position in different fields of applied sciences. In this study, we observe the dynamical behavior of nonlinear traveling waves for the M-fractional (3 + 1)-dimensional Wazwaz-Benjamin-Bona-Mohany (WBBM) equation. Novel exact traveling wave solutions in the form of trigonometric, hyperbolic and rational functions are derived using (1/G′), modified (G′/G2) and new extended direct algebraic methods with the help of symbolic soft computation. We guarantee that all the obtained results are new and verified the main equation. To promote the essential propagated features, some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the precise values to the parameters under the constrain conditions, and this provides useful information about the dynamical behavior. Further, bifurcation behavior of nonlinear traveling waves of the proposed equation is studied with the help of bifurcation theory of planar dynamical systems. It is also observed that the proposed equation support the nonlinear solitary
Citation - WoS: 24
Citation - Scopus: 24
New Trends in Fractional Dynamics
(Sage Publications Ltd, 2014) Baleanu, Dumitru; Chen, Wen; Sabatier, Jocelyn; Tenreiro Machado, Jose A.
Citation - WoS: 59
Citation - Scopus: 68
Spectrophotometric Quantitative Determination of Cilazapril and Hydrochlorothiazide in Tablets by Chemometric Methods
(Pergamon-elsevier Science Ltd, 2002) Baleanu, D; Dinç, E
Four chemometric methods were applied to simultaneous determination of cilazapril and hydrochlorothiazide in tablets. Classical least-square (CLS), inverse least-square (ILS), principal component regression (PCR) and partial least-squares (PLS) methods do not need any priori graphical treatment of the overlapping spectra of two drugs in a mixture. For all chemometric calibrations a concentration set of the random mixture consisting of the two drugs in 0.1 M HCl and methanol (1:1) was prepared. The absorbance data in the UV-Vis spectra were measured for the 15 wavelength points (from 222 to 276 nm) in the spectral region 210-290 nm considering the intervals of Deltalambda = 4 nm. The calibration of the investigated methods involves only absorbance and concentration data matrices. The developed calibrations were tested for the synthetic mixtures consisting of two drugs and using the Maple V software the chemometric, calculations were performed. The results of the methods were compared each other as well as with HPLC method and a good agreement was found. (C) 2002 Elsevier Science B.V. All rights reserved.
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.
Citation - WoS: 21
Citation - Scopus: 26
Robust Stabilization of Fractional-Order Chaotic Systems With Linear Controllers: Lmi-Based Sufficient Conditions
(Sage Publications Ltd, 2014) Kuntanapreeda, Suwat; Delavari, Hadi; Baleanu, Dumitru; Faieghi, Mohammad Reza
This paper is concerned with the problem of robust state feedback controller design to suppress fractional-order chaotic systems. A general class of fractional-order chaotic systems is considered and it is assumed that the systems' equations depend on bounded uncertain parameters. We transform the chaotic system equations into linear interval systems, and a sufficient stabilizability condition is derived in terms of linear matrix inequality (LMI). Then, an appropriate feedback gain is introduced to bring the chaotic states to the origin. Such design will result in a simple but effective controller. Several numerical simulations have been carried out to verify the effectiveness of the theoretic results.
Citation - Scopus: 5
A Necessary and Sufficient Condition for the Existence of Periodic Solutions of Linear Impulsive Differential Equations With Distributed Delay
(2007) Alzabut, J.O.; Alzabut, Jehad; Matematik
A necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive differential equations with distributed delay.
Citation - WoS: 51
Citation - Scopus: 56
Comparative Study of the Continuous Wavelet Transform, Derivative and Partial Least Squares Methods Applied To the Overlapping Spectra for the Simultaneous Quantitative Resolution of Ascorbic Acid and Acetylsalicylic Acid in Effervescent Tablets
(Elsevier Science Bv, 2005) Ozdemir, A; Baleanu, D; Dinç, E
The simultaneous spectrophotometric determination of ascorbic acid (AA) and acetylsalicylic acid (ASA) in effervescent tablets in the presence of the overlapping spectra was accomplished by the continuous wavelet transform (CWT), derivative spectrophotometry (DS) and partial least squares (PLS) approaches without using any chemical pre-treatment. CWT and DS calibration equations for AA and ASA were obtained by measuring the CWT and DS amplitudes corresponding to zero-crossing points of spectra obtained by plotting continuous wavelet coefficients and first-derivative absorbance values versus the wavelengths, respectively. The PLS calibration was constructed by using the concentration set and its full absorbance data consisting of 850 points from 220 to 305 urn in the range of 210-310 nun. These three methods were tested by analyzing the synthetic mixtures of the above drugs and they were applied to the real samples containing two commercial pharmaceutical preparations of subjected drugs. A comparative study was carried out by using the experimental results obtained from three analytical methodologies and precise and accurate results were obtained. (c) 2004 Published by Elsevier B.V.
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: 2
Citation - Scopus: 3
(Δ Backward Difference )^{Backward Difference}-pachpatte Dynamic Inequalities Associated With Leibniz Integral Rule on Time Scales With Applications
(Mdpi, 2022) Baleanu, Dumitru; Awrejcewicz, Jan; El-Deeb, Ahmed A.
We prove some new dynamic inequalities of the Gronwall-Bellman-Pachpatte type on time scales. Our results can be used in analyses as useful tools for some types of partial dynamic equations on time scales and in their applications in environmental phenomena and physical and engineering sciences that are described by partial differential equations.

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