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Solution approximations for a mathematical model of relativistic electrons with beta derivative

Applied Mathematics(A Journal of Chinese Universities) 2024年第3期39卷 469-485页

作者： Ibrahim Yalcinkaya Orkun Tasbozan Ali Kurt Hijaz Ahmad Department of Mathematics and Computer Sciences Faculty of ScienceNecmettin Erbakan UniversityKonyaTurkey Department of Mathematics Faculty of Science and LiteratureHatay Mustafa Kemal UniversityHatayTurkey Department of Mathematics Faculty of SciencePamukkale UniversityDenizliTurkey Near East University Operational Research Center in HealthcareTRNC Mersin 10Nicosia99138Turkey Department of Mathematics Faculty of ScienceIslamic University of MadinahMadinahSaudi Arabia

The main aim of this paper is to obtain the exact and semi-analytical solutions of the nonlinear Klein-Fock-Gordon(KFG)equation which is a model of relativistic electrons arising in the laser thermonuclear fusion with beta *** this purpose,both the modified extended tanh-function(mETF)method and the homotopy analysis method(HAM)are *** applying the mETF the chain rule for beta derivative and complex wave transform are used for obtaining the exact *** advantage of this procedure is that discretization or normalization is not *** applying the mETF,the exact solutions are ***,by applying the HAM semi-analytical results for the considered equation are *** HAM?curve gives us a chance to find the suitable value of the for the convergence of the solution ***,comparative graphical representations are given to show the effectiveness,reliability of the *** results show that the m ETF and HAM are reliable and applicable tools for obtaining the solutions of non-linear fractional partial differential equations that involve beta *** study can bring a new perspective for studies on fractional differential *** the other hand,it can be said that scientists can apply the considered methods for different mathematical models arising in physics,chemistry,engineering,social sciences and *** involves fractional *** the results may cause a new insight who studies on relativistic electron modelling.

关键词： Klein-Fock-Gordon(KFG)equation beta derivative semi-analytical solution exact solution

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Soliton solutions for time fractional ocean engineering models with beta derivative

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Journal of Ocean Engineering and Science 2022年第5期7卷 444-448页

作者： Ibrahim Yalçınkaya Hijaz Ahmad Orkun Tasbozan Ali Kurt Department of Mathematics and Computer Sciences Faculty of ScienceNecmettin Erbakan UniversityKonyaTurkey Department of Basic Sciences University of Engineering and TechnologyPeshawarPakistan Department of Mathematics Faculty of Science and LiteratureHatay Mustafa Kemal UniversityHatayTurkey Department of Mathematics Faculty of Science and LiteraturePamukkale UniversityDenizliTurkey

In this study,the authors obtained the soliton and periodic wave solutions for time fractional symmetric regularized long wave equation(SRLW)and Ostrovsky equation(OE)both arising as a model in ocean *** this aim modified extended tanh-function(mETF)is *** using this method,chain rule is employed to turn fractional nonlinear partial differential equation into the nonlinear ordinary differential equation in integer *** to the chain rule,there is no further requirement for any normalization or *** derivative which involves fractional term is used in considered mathematical *** the exact solutions of these equations is very important for knowing the wave behavior in ocean engineering models.

关键词： Symmetric regularized long wave equation beta derivative Ostrovsky equation Analytical solution Soliton solutions Periodic wave solution

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A unique computational investigation of the exact traveling wave solutions for the fractional-order Kaup-Boussinesq and generalized Hirota Satsuma coupled KdV systems arising from water waves and interaction of long waves

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Journal of Ocean Engineering and Science 2024年第5期9卷 437-453页

作者： Xiaofeng Wang Xiao-Guang Yue Mohammed K.A.Kaabar Arzu Akbulut Melike Kaplan Shenzhen University ShenzhenChina Department of Computer Science and Engineering European University CyprusNicosiaCyprus Institute of Mathematical Sciences Faculty of ScienceUniversity of MalayaKuala Lumpur 50603Malaysia Department of Mathematics and Statistics Washington State UniversityPullmanWA 99163USA Jabalia Camp United Nations Relief and Works Agency(UNRWA)Palestinian Refugee CampGaza Strip JabalyaPalestine Mathematics-Computer Department Art-Science FacultyEski¸s ehir Osmangazi UniversityEski¸s ehirTurkey Department of Computer Engineering Faculty of Engineering and ArchitectureKastamonu UniversityKastamonuTurkey

A novel technique,named auxiliary equation method,is applied in this research work for obtaining new traveling wave solutions for two interesting proposed systems:the Kaup-Boussinesq system and generalized Hirota-Satsuma coupled KdV system with beta time fractional *** solutions were obtained using MAPLE *** technique shows a great potential to be applied in solving various nonlinear fractional differential equations arising from mathematical physics and ocean *** a standard equation has not been used as an auxiliary equation for this technique,different and novel solutions are obtained via this technique.

关键词： Symbolic computation Fractional differential equations beta derivative Auxiliary equation method Solitary solutions Nonlinear equations

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