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Oblique closed form solutions of some important fractional evolution equations via the modified kudryashov method arising in physical problems

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Journal of Ocean Engineering and Science 2018年第3期3卷 244-252页

作者： F.Ferdous M.G.Hafez Department of Mathematics Chittagong University of Engineering and TechnologyChittagong4349Bangladesh

The paper deals with the obliquely propagating wave solutions of fractional nonlinear evolution equations(NLEEs)arising in science and *** conformable time fractional(2+1)-dimensional extended Zakharov-Kuzetsov equation(EZKE),coupled space-time fractional(2+1)-dimensional dispersive long wave equation(DLWE)and space-time fractional(2+1)-dimensional Ablowitz-Kaup-Newell-Segur(AKNS)equation are considered to investigate such physical *** modified kudryashov method along with the properties of conformable and modified Riemann-Liouville derivatives is employed to construct the oblique wave solutions of the considered *** obtained results may be useful for better understanding the nature of internal oblique propagating wave dynamics in ocean engineering.

关键词： Fractional nonlinear evolution equations Conformable derivative modified kudryashov method Oblique wave solutions

The Traveling Wave Solutions of Space-Time Fractional Partial Differential Equations by modified kudryashov method

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Journal of Applied Mathematics and Physics 2020年第11期8卷 2683-2690页

作者： Md. Mahfujur Rahman Umme Habiba Md. Abdus Salam Mousumi Datta Department of Mathematics Mawlana Bhashani Science and Technology University Tangail Bangladesh

In this paper, the modified kudryashov method is employed to find the traveling wave solutions of two well-known space-time fractional partial differential equations, namely the Zakharov Kuznetshov Benjamin Bona Mahony equation and Kolmogorov Petrovskii Piskunov equation, and as a helping tool, the sense of modified Riemann-Liouville derivative is also used. The propagation properties of obtained solutions are investigated where the graphical representations and justifications of the results are done by mathematical software Maple.

关键词： Traveling Wave Solutions modified kudryashov method Zakharov Kuznetshov Benjamin Bona Mahony (ZKBBM) Equation Kolmogorov Petrovskii Piskunov (KPP) Equation

Density-Dependent Conformable Space-time Fractional Diffusion-Reaction Equation and Its Exact Solutions

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Communications in Theoretical Physics 2018年第1期69卷 1-4页

作者： Kamyar Hosseini Peyman Mayeli Ahmet Bekir Ozkan Guner Department of Mathematics Rasht Branch Islamic Azad University Young Researchers and Elite Club Lahijan Branch Islamic Azad University Department of Mathematics and Computer Art-Science Faculty Eskisehir Osmangazi University Department of International Trade Faculty of Economics and Administrative Sciences Cankiri Karatekin University

In this article, a special type of fractional differential equations(FDEs) named the density-dependent conformable fractional diffusion-reaction(DDCFDR) equation is studied. Aforementioned equation has a significant role in the modelling of some phenomena arising in the applied science. The well-organized methods, including the exp(-φ(ε))-expansion and modified kudryashov methods are exerted to generate the exact solutions of this equation such that some of the solutions are new and have been reported for the first time. Results illustrate that both methods have a great performance in handling the DDCFDR equation.

关键词： density-dependent conformable fractional diffusion-reaction equation exp(-Ф(ε) )-expansion method modified kudryashov method exact solutions

New soliton wave solutions of a(2+1)-dimensional Sawada-Kotera equation

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Journal of Ocean Engineering and Science 2023年第5期8卷 527-532页

作者： Kong Debin Hadi Rezazadeh Najib Ullah Javad Vahidi Kalim U.Tariq Lanre Akinyemi Department of Mathematics Yantai Nanshan UniversityShandong 265713China Faculty of Engineering Technology Amol University of Special Modern TechnologiesAmolIran Department of Mathematics COMSATS University IslamabadIslamabad 45550Pakistan Department of Applied Mathematics Iran University of Science and TechnologyTehranIran Department of Mathematical Sciences University of South AfricaPretoria 0002South Africa Department of Mathematics Mirpur University of Science and TechnologyMirpur 10250(AJK)Pakistan Department of Mathematics Lafayette CollegeEastonPennsylvaniaUnited States

In this work,we studied a(2+1)-dimensional Sawada-Kotera equation(SKE).This model depicts non-linear wave processes in shallow water,fluid dynamics,ion-acoustic waves in plasmas and other phe-nomena.A couple of well-established techniques,the Bäcklund transformation based on the modified kudryashov method,and the Sardar-sub equation method are applied to obtain the soliton wave solution to the(2+1)-dimensional *** illustrate the behavior of the nonlinear model in an appealing fashion,a variety of travelling wave solutions are formed,such as contour,2D,and 3D *** pro-posed approaches are proved more convenient and dominant for getting analytical solutions and can also be implemented to a variety of physical models representing nonlinear wave phenomena.

关键词： modified kudryashov method Sardar-sub equation method Bäcklund transformation(2+1)-dimensional SKE Soliton wave solutions

Exact Solutions to (3+1) Conformable Time Fractional Jimbo–Miwa,Zakharov–Kuznetsov and modified Zakharov–Kuznetsov Equations

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Communications in Theoretical Physics 2017年第5期67卷 479-482页

作者： Alper Korkmaz Department of Mathematics Cankiri Karatekin UniversityCankiriTurkey

Exact solutions to conformable time fractional (3+1)-dimensional equations are derived by using the modified form of the kudryashov method. The compatible wave transformation reduces the equations to an ODE with integer orders. The predicted solution of the finite series of a rational exponential function is substituted into this *** resultant polynomial equation is solved by using algebraic operations. The method works for the Jimbo–Miwa, the Zakharov–Kuznetsov, and the modified Zakharov–Kuznetsov equations in conformable time fractional forms. All the solutions are expressed in explicit forms.

关键词： fractional (3+1)-dimensional Jimbo–Miwa equation fractional modified Zakharov–Kuznetsov equation modified kudryashov method fractional Zakharov–Kuznetsov equation exact solutions

Two efficient reliable methods for solving fractional fifth order modified Sawada-Kotera equation appearing in mathematical physics

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Journal of Ocean Engineering and Science 2016年第3期1卷 219-225页

作者： S.Saha Ray S.Sahoo National Institute of Technology Department of MathematicsRourkela 769008India

The present paper deals with two reliable efficient methods ***-sech method and modified kudryashov method,which are used to solve time-fractional nonlinear evolution *** delineating the legitimacy of proposed methods,we employ it to the time-fractional fifth-order modified Sawada-Kotera *** a consequence,we effectively obtained more new exact solutions for time-fractional fifth-order modified Sawada-Kotera *** have also presented the numerical simulations for time-fractional fifth-order modified Sawada-Kotera equation by means of three dimensional plots.

关键词： Time-fractional fifth-order modified Sawada-Kotera equation Local fractional calculus Tanh-sech method modified kudryashov method