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Exact solutions of nonlinear fractional differential equations by (G'/G)-expansion method

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Chinese Physics B 2013年第11期22卷 140-145页

作者： Ahmet bekir zkan Güner Eskisehir Osmangazi university Art-Science Faculty Department of Mathematics-Computer Dumlup nar university School of Applied Sciences Department of Management Information Systems

In this paper, we use the fractional complex transform and the （G＇/G）-expansion method to study the nonlinear fractional differential equations and find the exact solutions. The fractional complex transform is proposed to convert a partial fractional differential equation with Jumarie＇s modified Riemann-Liouville derivative into its ordinary differential equation. It is shown that the considered transform and method are very efficient and powerful in solving wide classes of nonlinear fractional order equations.

关键词： (G'/G)-expansion method time-fractional Burgers equation fractional-order biological popula-tion model space-time fractional Whitham-Broer-Kaup equations

Investigation of soliton solutions with different wave structures to the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation

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Communications in Theoretical Physics 2020年第3期72卷 7-13页

作者： M S Osman K u Tariq Ahmet bekir A Elmoasry Nasser S Elazab M Younis Mahmoud Abdel-Aty Department of Mathematics Faculty of ScienceCairo UniversityGizaEgypt Department of Mathematics Faculty of Applied ScienceUmm Alqura UniversityMakkah 21955Saudi Arabia School of Mathematics and Statistics Huazhong University of Science and TechnologyWuhan 430074China Department of Mathematics Mirpur University of Science and TechnologyMirpur(AJK)10250Pakistan Neighbourhood of Akcaglan Imarli StreetNumber:28/426030EskisehirTurkey Mathematics department College of ScienceMajmaah UniversitySaudi Arabia Punjab university College of Information Technology University of the PunjabLahore 54590Pakistan Department of Mathematics Faculty of ScienceSohag UniversitySohagEgypt Applied Science university Bahrain

The principal objective of this article is to construct new and further exact soliton solutions of the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets and explains their ordering in ferromagnetic *** solutions are exerted via the new extended FAN sub-equation *** successfully obtain dark,bright,combined bright-dark,combined dark-singular,periodic,periodic singular,and elliptic wave solutions to this equation which are interesting classes of nonlinear excitation presenting spin dynamics in classical and semi-classical continuum Heisenberg systems.3D figures are illustrated under an appropriate selection of *** applied technique is suitable to be used in gaining the exact solutions of most nonlinear partial/fractional differential equations which appear in complex phenomena.

关键词： soliton solutions Heisenberg ferromagnetic equation FAN sub-equation method

The Exp-function Method for Some Time-fractional Differential Equations

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IEEE/CAA Journal of Automatica Sinica 2017年第2期4卷 315-321页

作者： Ahmet bekir Ozkan Guner Adem Cevikel Department of Mathematics-computer Eskisehir Osmangazi University Department of International Trade Cankiri Karatekin University Department of Mathematics Education Yildiz Technical University

In this article, the fractional derivatives in the sense of modified Riemann-Liouville derivative and the Exp-function method are employed for constructing the exact solutions of nonlinear time fractional partial differential equations in mathematical physics. As a result, some new exact solutions for them are successfully established. It is indicated that the solutions obtained by the Exp-function method are reliable, straightforward and effective method for strongly nonlinear fractional partial equations with modified Riemann-Liouville derivative by Jumarie's. This approach can also be applied to other nonlinear time and space fractional differential equations.

关键词： Exact solution exp-function method fractional differential equation

Dynamic simulation of an opencast coal mine: a case study

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International Journal of Coal Science & Technology 2020年第1期7卷 164-181页

作者： Kesavan Muniappen bekir Genc School of Mining Engineering University of the WitwatersrandJohannesburgSouth Africa

Dynamic simulations are powerful tools,but only if they are developed using the correct methodology,and with information that has been *** houses rely on simulation to confirm that complex,integrated systems can achieve design capacity before investment decisions are *** conducted in the realm of validation can make an invaluable contribution to the success of future projects undertaken around the *** mine a life of mine extension project was approved for implementation when export coal prices were on the low end of the price *** dynamic simulation of the full materials handling value chain conducted during the project feasibility study in 2016 was of utmost importance and provided assurance to the project review team that annual production targets can be *** simulation development methodology was based on a unique approach that reduced time spent on the *** completion of project construction and commissioning in 2018,it was essential to validate the simulation,which could lead to the adoption of this approach on future *** paper explains the steps taken to validate the dynamic *** case study confirmed that dynamic simulation can add value and predict mining system performance,such that informed decisions can be made.

关键词： Simulation Gensym G2 System performance Life of mine Coal mining

Singular 1-soliton and Periodic Solutions to the Nonlinear Fisher-Type Equation with Time-Dependent Coefficients

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Communications in Theoretical Physics 2016年第4期65卷 405-409页

作者： Ozkan Guner Ahmet bekir Cankiri Karatekin university Faculty of Economics and Administrative SciencesDepartment of International Trade Eskisehir Osmangazi university Art-Science FacultyDepartment of Mathematics and Computer Science

In this article,we establish exact solutions for the variable-coefficient Fisher-type *** solutions are obtained by the modified sine-cosine method and ansatz *** soliton and periodic solutions and topological as well as the singular 1-soliton solution are obtained with the aid of the ansatz *** solutions are important for the explanation of some practical physical *** obtained results show that these methods provide a powerful mathematical tool for solving nonlinear equations with variable coefficients.

关键词： modified sine-cosine method ansatz method the variable-coefficient Fisher-type equation

Exact solutions of some fractional differential equations arising in mathematical biology

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International Journal of Biomathematics 2015年第1期8卷 29-45页

作者： Ozkan Guner Ahmet bekir Department of Management Information Systems School of Applied Sciences Dumlup~nar University Kutahya Turkey Department of Mathematics and Computer Art-Science Faculty Eskisehir Osmangazi University Eskisehir Turkey

In the last decades Exp-function method has been used for solving fractional differential equations. In this paper, we obtain exact solutions of fractional generalized reaction Duff- ing model and nonlinear fractional diffusion-reaction equation. The fractional derivatives are described in the modified Riemann-Liouville sense. The fractional complex trans- form has been suggested to convert fractional-order differential equations with modified Riemann-Liouville derivatives into integer-order differential equations, and the reduced equations can be solved by symbolic computation.

关键词： Fractional partial differential equation exact solutions Exp-function method modified Riemann-Liouville derivative.

Response of hydrological drought to meteorological drought in the eastern Mediterranean Basin of Turkey

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Journal of Arid Land 2021年第5期13卷 470-486页

作者： Türkan BAYER ALTIN bekir N ALTIN Department of Geography Faculty of Science and LettersNiğdeÖmer Halisdemir UniversityNiğde 51240Turkey

The hydrographic eastern Mediterranean Basin of Turkey is a drought sensitive *** basin is an important agricultural area and it is necessary to determine the extent of extreme regional climatic changes as they occur in this ***’s correlation coefficient was used to show the correlation between standardized precipitation index(SPI)and standardized streamflow index(SSI)values on different time *** from five meteorological stations and seven stream gauging stations in four sub-basins of the eastern Mediterranean Basin were analyzed over the period from 1967 to *** correlation between SSI and SPI indicated that in response to meteorological drought,hydrological drought experiences a one-year delay then occurs in the following *** is more evident at all stations from the mid-1990 *** main factor causing hydrological drought is prolonged low precipitation or the presence of a particularly dry *** showed that over a long period(12 months),hydrological drought is longer and more severe in the upper part than the lower part of the *** to SPI-12 values,an uninterrupted drought period is observed from 2002–2003 to 2008–*** indicated that among the drought events,moderate drought is the most common on all timescales in all sub-basins during the past 51 ***-term dry periods with moderate and severe droughts are observed for up to 10 years or more since the late 1990 s,especially in the upper part of the *** precipitation increases in late autumn and early winter,the stream flow also increases and thus the highest and most positive correlation values(0.26–0.54)are found in *** values(ranging between–0.11 and–0.01)are weaker and negative in summer and autumn due to low *** is more evident at all stations in *** relation between hydrological and meteorological droughts is more evident,with the correlation values above 0.50 on longer timescales(12-and 24-month

关键词： meteorological drought hydrological drought standardized precipitation index(SPI) standardized streamflow index(SSI) eastern Mediterranean Basin

Constant frequency operation of parallel resonant converter for constant-current constant-voltage battery charger applications

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Journal of Modern Power Systems and Clean Energy 2019年第1期7卷 186-199页

作者： Taha Nurettin GüCIN Muhammet BIBEROGLu bekir FINCAN Energy Systems Engineering Department University of Yalova Electrical Engineering Department Istanbul Technical University

This paper proposes a design and control approach to parallel resonant converter(PRC) based battery *** proposed approach is particularly suitable for the constant-current constant-voltage(CC-CV)charging method, which is the most commonly utilized *** the PRC is operated at two different frequencies for each CC and CV charging modes, this approach eliminates the need for complicated control techniques such as the frequency-control and *** proposed method not only simplifies the design and implementation processes of the converter unit but also simplifies the design of output filter configuration and decreases the number of the required components for the control of the *** proposed method is confirmed by two experimental *** results show that the designed charger circuit ensured a very stable constant current in CC charging phase, where the charging current is fixed to 1.75 *** a voltage increase in CV phase is observed, the charger circuit is able to decrease the charging current to 0.5 A in CV phase, as depicted in battery *** efficiency of the charger is figured out to be in the range of 86%-93% in the first setup, while it is found to be in the range of 78%-88% in the second setup,where a high frequency transformer is employed.

关键词： Resonant converter Parallel resonant converter Battery charger Constant-current constant-voltage(CC-CV)charging

ELECTRORHEOLOGY AND CREEP-RECOVERY BEHAVIOR OF CONDuCTING POLYTHIOPHENE/POLY(OXYMETHYLENE)-BLEND SuSPENSIONS

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Chinese Journal of Polymer Science 2012年第1期30卷 16-25页

作者： Ozlem Erol H.Ibrahim unal bekir Sari Smart Materials Research Lab Chemistry Department Gazi UniversityAnkaraTurkey

Electrorheological properties and creep-recovery behavior of polythiophene/polyoxymethylene-blend having PT（50%）/POM（50%） composition were *** size,conductivity and dielectric values were measured to be 24.77μm,3.85×10^（-5） S·m^（-1） and 26.75,*** ratio was measured to be 64%at the end of 16 *** effects of dispersed particle volume fraction,external electric field strength,shear rate,frequency and temperature on ER properties and storage modulus of PT/POM-blend/silicone oil（SO） suspensions were *** were observed in the electric field viscosities of the suspensions and thus they were classified as a smart *** thinning non-Newtonian viscoelastic behavior was determined for PT/POM-blend/SO ***,time-dependent deformation was examined by creep-recovery tests and recoverable viscoelastic deformation established.

关键词： Conducting polythiophene/poly(oxymethylene) Blends Electrorheogical fluids Creep-recovery behavior