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Solving Space-Time Fractional Differential Equations by Using Modified Simple Equation Method

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Communications in Theoretical Physics 2016年第5期65卷 563-568页

作者： Melike Kaplan arzu akbulut Ahmet Bekir Eskisehir Osmangazi University Art-Science Faculty Department of Mathematics-Computer

In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation *** proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.

关键词： symbolic computation exact solution space-time fractional differential equation space-time fractional Klein–Gordon equation the space-time fractional breaking soliton equations

New exact solutions of the Mikhailov-Novikov-Wang equation via three novel techniques

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Journal of Ocean Engineering and Science 2023年第1期8卷 103-110页

作者： arzu akbulut Melike Kaplan Mohammed K.A.Kaabar Mathematics-Computer Department Art-Science FacultyEski¸s ehir Osmangazi UniversityEski¸s ehirTurkey Department of Computer Engineering Engineering and Architecture FacultyKastamonu UniversityKastamonuTurkey Institute of Mathematical Sciences Faculty of ScienceUniversity of MalayaKuala Lumpur 50603Malaysia

The current work aims to present abundant families of the exact solutions of Mikhailov-Novikov-Wang equation via three different *** adopted methods are generalized Kudryashov method(GKM),exponential rational function method(ERFM),and modified extended tanh-function method(METFM).Some plots of some presented new solutions are represented to exhibit wave *** results in this work are essential to understand the physical meaning and behavior of the investigated equation that sheds light on the importance of investigating various nonlinear wave phenomena in ocean engineering and *** equation provides new insights to understand the relationship between the integrability and water waves’phenomena.

关键词： Exact solutions Generalized Kudryashov method Modified extended tanh-function method Symbolic computation PDEs

New conservation laws and exact solutions of the special case of the fifth-order KdV equation

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Journal of Ocean Engineering and Science 2022年第4期7卷 377-382页

作者： arzu akbulut Melike Kaplan Mohammed K.A.Kaabar Department of Mathematics-Computer Art-Science FacultyEskisehir Osmangazi UniversityEskisehirTurkey Department of Mathematics Art-Science FacultyKastamonu UniversityKastamonuTurkey Institute of Mathematical Sciences Faculty of ScienceUniversity of MalayaKuala Lumpur 50603Malaysia

The current study deals with the Kaup-Kupershmidt(KK)equation to construct formal Lagrangian,con-servation laws,and exact *** is basically a special case of the 5th-order KdV *** conservation laws obtained by using the conservation theorem are trivial conservation *** addition,exact solutions are found via the modified simple equation(MSE)*** a suitable value of solu-tions,the 3D surfaces have been plotted using *** plots giving novel exact solutions are made to reveal important wave *** obtained results in this work concerning our investigated equation are essential to explain many physical and oceanographic applications involving ocean gravity waves and many other related phenomena.

关键词： Conservation laws Exact solutions Symbolic computation Modified simple equation method

New solitary waves and exact solutions for the fifth-order nonlinear wave equation using two integration techniques

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Journal of Ocean Engineering and Science 2023年第5期8卷 475-480页

作者： Ahmed H.Arnous Mohammad Mirzazadeh Lanre Akinyemi arzu akbulut Department of Physics and Engineering Mathematics Higher Institute of EngineeringEl Shorouk AcademyCairoEgypt Department of Engineering Sciences Faculty of Technology and EngineeringEast of GuilanUniversity of GuilanRudsar-VajargahIran Department of Mathematics Lafayette CollegeEastonPennsylvaniaUSA Department of Mathematics Computer Faculty of Art ScienceEskisehir Osmangazi UniversityEskisehirTurkey

In this paper,we discussed the enhanced Kudryashov’s and general projective Riccati equations tech-niques for obtaining exact solutions to the fifth-order nonlinear water wave(FONLWWE)*** the enhanced Kudryashov’s method,we were able to achieve solitary wave and singular soliton ***-shock hybrid wave,singular soliton,and periodic wave solutions were discovered when we em-ployed the general projective Riccati equations *** can say the given methods are effective and powerful for obtaining exact *** findings in this paper are critical for explaining a wide range of scientific and oceanographic applications involving ocean gravity waves and other related phenomena.

关键词： Enhanced Kudryashov method Riccati equation Water waves Fifth-order nonlinear model Solitons

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