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Analytical Approach to Fractional Zakharov-Kuznetsov Equations by He's Homotopy Perturbation Method

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Communications in Theoretical Physics 2010年第6期53卷 1005-1010页

作者： ahmet yildirim Yagmur Gülkanat Ege University Department of Mathematics

The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.

关键词： homotopy perturbation method fractional Zakharov-Kuznetsov equations fractional calculus Caputo sense

Analytical Approach to Space- and *** Burgers Equations

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Chinese Physics Letters 2010年第9期27卷 38-41页

作者： ahmet yildirim Syed Tauseef Mohyud-Din Department of Mathematics Ege University 35100 Bornova-Izmir Turkey HITEC University Taxila Cantt Pakistan

A scheme is developed to study numerical solution of the space- and time-fractional Burgers equations under initial conditions by the homotopy analysis method. The fractional derivatives are considered in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical solutions are calculated for the fractional Burgers equation to show the nature of solution as the fractional derivative parameter is changed.

关键词： BURGERS' equation SPACE & time DIFFERENTIAL equations -- Numerical solutions HOMOTOPY theory FRACTIONAL calculus MATHEMATICAL analysis

Poincaré-MacMillan Equations of Motion for a Nonlinear Nonholonomic Dynamical System

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Chinese Physics Letters 2012年第3期29卷 132-134页

作者： Amjad Hussain Syed Tauseef Mohyud-Din ahmet yildirim Department of Mathematics Zhejiang UniversityHangzhou 310027 Department of Mathematics HITEC UniversityTaxila Cantt Pakistan Department of Mathematics Ege University35100 Bornova IzmirTurkey University of South Florida Department of Mathematics and StatisticsTampaFL 33620-5700USA

MacMillan's equations are extended to Poincaré's formalism,and MacMillan's equations for nonlinear nonholonomic systems are obtained in terms of Poincaré*** equivalence of the results obtained here with other forms ... 详细信息

关键词： Poincaré parameters MacMillan

Solution to the MHD flow over a non-linear stretching sheet by homotopy perturbation method

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Science China(Physics,Mechanics & Astronomy) 2011年第2期54卷 342-345页

作者： RAFTARI Behrouz MOHYUD-DIN Syed Tauseef yildirim ahmet Department of Mathematics Islamic Azad UniversityKermanshah branch Taxila Cantt HITEC University Department of Mathematics Ege University

In this study,by means of homotopy perturbation method(HPM) an approximate solution of the magnetohydrodynamic(MHD) boundary layer flow is *** main feature of the HPM is that it deforms a difficult problem into a set of problems which are easier to *** produces analytical expressions for the solution to nonlinear differential *** obtained analytic solution is in the form of an infinite power *** this work,the analytical solution obtained by using only two terms from HPM *** with the exact solution and the solution obtained by the Pade approximants and shooting method show the high accuracy,simplicity and efficiency of this method.

关键词： boundary layer flow magnetohydrodynamics flow(MHD) nonlinear differential equations homotopy perturbation method

Dynamics of an SAIQR influenza model of fractional order via convex incidence rate

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International Journal of Modeling, Simulation, and Scientific Computing 2020年第4期11卷 177-189页

作者： Ghaus ur Rahman ahmet yildirim Fazal Haq Emile F.Doungmo Goufo Department of Mathematics and Statistics University of Swat Pakistan Department of Mathematics Bornova-Azmir¨Ege UniversityTurkey Department of Mathematics Hazara University MansehraPakistan Department of Mathematical Sciences University of South Africa FloridaSouth Africa

Influenza A-virus infection represents a global threat causing seasonal outbreaks andpandemics. Among the global threats creating seasonal outbreak, Influenza “A-virus”infection is a dominating theme nowadays. Using the theory of fractional calculus, thisstudy considers an influenza model for quantitative study via the Laplace AdomianDecomposition Method (LADM). We proceed to explore the role of LADM on the proposed model. The method is described and explained for the proposed model whileproviding some plots to present the behavior of the disease.

关键词： Influenza disease mathematical models fractional derivatives Laplace-Adomian decomposition method analytical solution.

Optical Properties of Aligned Nematic Liquid Crystals in Electric Field

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Journal of Modern Physics 2011年第4期2卷 248-255页

作者： Suleyman Yilmaz Halide Melik Firat Angay Mehriban Emek ahmet yildirim 不详

In this study, the optical transmittance of aligned nematic liquid crystals (ANLCs) was investigated in terms of temperature variations through electrooptic effects under DC electric field. The optical transmittances of the planar and homeotropically aligned liquid crystal cells, which were prepared by conventional rubbing and photolithographic technique on the polyimide thin films for molecular alignment, were measured in their phase transition region. The results of measurement for both orientations, the distribution curve of the optical transmittance exhibits displacement toward to low level at the beginning and then to high level by the temperature variations, while the electric field increases. It was also observed that the domain structure of the materials were affected considerably by the applied electric field and phase transition region of the aligned structures had broader range than by the pure crystalline structure and its phase transition temperature was changed by the molecular anisotropy. Finally, in photolithographic method strong bonds between the molecules and the orienting surface were observed in high contrast to rubbing method.

关键词： Liquid Crystals Thin Films Photolithography Optical Properties

Chaos in Time Series of Sakarya River Daily Flow Rate

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Journal of Applied Mathematics and Physics 2016年第10期4卷 1849-1858页

作者： Haci ahmet yildirim Avadis Simon Hacinliyan Ergun Eray Akkaya Cercis Ikiel Department of Physics Sakarya University Adapazari Turkey Department of Physics Yeditepe University Istanbul Turkey Department of Information Systems and Technologies Yeditepe University Istanbul Turkey Department of Geography Sakarya University Adapazari Turkey

In this study, possible low dimensional chaotic behavior of Sakarya river flow rates is investigated via nonlinear time series techniques. To reveal the chaotic dynamics, the maximal positive Lyapunov exponent is calculated from the reconstructed phase space, which is obtained using the phase space reconstruction method. The method reconstructs a phase space from the scalar time series, which depicts the real system’s invariants Positive values, because the Lyapunov exponent values calculated using the appropriate software program indicate possibility of chaotic behavior. Analyzed data involve the monthly average flow rates of eleven main branches of Sakarya River through the years 1960-2000.

关键词： Chaos Theory Time Series Analysis Lyapunov Exponent Mutual Information False Nearest Neighbors

A Comparative Study of Analytical Solutions to the Coupled Van-der-Pol’s Non-linear Circuits Using the He’s Method(HPEM)and(BPES)

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Circuits and Systems 2011年第3期2卷 196-200页

作者： Huseyin Kocak ahmet yildirim Dahong Zhang Karem Boubaker Syed Tauseef Mohyud-Din Department of Mathematics Ege UniversityBornova–IzmirTurkey Department of Physics South China UniversityGuangzhouChina Ecole Superieure des Sciences et Techniques de Tunis University of TunisTunisTunisia Department of Basic Sciences HITEC UniversityTaxila CanttPakistan

In this paper, the He’s parameter-expanding method (HPEM) and the 4q-Boubaker Polynomials Expansion Scheme (BPES) are used in order to obtain analytical solutions to the non-linear modified Van der Pol’s oscillating circuit equation. The resolution protocols are applied to the ordinary Van der Pol equation, which annexed to conjoint delayed feedback and delay-related damping terms. The results are plotted, and compared with exact solutions proposed elsewhere, in order to evaluate accuracy.

关键词： Van-der-Pol’s Oscillating Circuit Delayed Feedback Damping BPES HPEM Exact Solutions Electrical Triode-Valve Circuit

Optical Properties of Aligned Nematic Liquid Crystals in Electric Field

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