检索结果-南通市图书馆

Communications in Theoretical Physics 2024年第3期76卷 70-83页

作者： Di Liu qiongya Gu Lizhen Wang Center for Nonlinear Studies School of MathematicsNorthwest UniversityXi'an710127China

In this paper,two types of fractional nonlinear equations in Caputo sense,time-fractional Newell–Whitehead equation(FNWE)and time-fractional generalized Hirota–Satsuma coupled KdV system(HS-cKdVS),are investigated by means of the q-homotopy analysis method(q-HAM).The approximate solutions of the proposed equations are constructed in the form of a convergent series and are compared with the corresponding exact solutions.Due to the presence of the auxiliary parameter h in this method,just a few terms of the series solution are required in order to obtain better approximation.For the sake of visualization,the numerical results obtained in this paper are graphically displayed with the help of Maple.

关键词： fractional Newell-Whitehead equation fractional generalized Hirota-Satsuma coupled KdV system approximate solution q-homotopy analysis method

Analytical and approximate solutions of nonlinear Schrödinger equation with higher dimension in the anomalous dispersion regime

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Journal of Ocean Engineering and Science 2022年第2期7卷 143-154页

作者： Lanre Akinyemi Mehmet Senol M.S.Osman Department of Mathematics Lafayette CollegeEastonPAUSA Nev¸s ehir HacıBekta¸s Veli University Department of MathematicsNev¸s ehirTurkey Department of Mathematics Faculty of ScienceCairo UniversityGiza 12613Egypt

The generalized Riccati equation mapping method(GREMM)is used in this paper to obtain different types of soliton solutions for nonlinear Schrödinger equation with higher dimension that existed in the regimes of anomalous dispersion.Later,we use the q-homotopy analysis method combined with the Laplace transform(q-HATM)to obtain approximate solutions of the bright and dark optical solitons.The q-HATM illustrates the solutions as a rapid convergent series.In addition,to show the physical behavior of the solutions obtained by the proposed techniques,the graphical representation has been provided with some parameter values.The findings demonstrate that the proposed techniques are useful,efficient and reliable mathematical method for the extraction of soliton solutions.

关键词： q-homotopy analysis method Generalized Riccati equation mapping method Laplace transform

Novel approach for modified forms of Camassa–Holm and Degasperis–Procesi equations using fractional operator

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2020年第10期72卷 12-18页

作者： P Veeresha D G Prakasha Department of Mathematics Karnatak UniversityDharwad-580003KarnatakaIndia Department of Mathematics Faculty of ScienceDavangere UniversityShivagangothriDavangere 577007KarnatakaIndia

In the present study,we consider the q-homotopy analysis transform method to find the solution for modified Camassa–Holm and Degasperis–Procesi equations using the Caputo fractional operator.Both the considered equations are nonlinear and exemplify shallow water behaviour.We present the solution procedure for the fractional operator and the projected solution procedure gives a rapidly convergent series solution.The solution behaviour is demonstrated as compared with the exact solution and the response is plotted in 2D plots for a diverse fractional-order achieved by the Caputo derivative to show the importance of incorporating the generalised concept.The accuracy of the considered method is illustrated with available results in the numerical simulation.The convergence providence of the achieved solution is established in?-curves for a distinct arbitrary order.Moreover,some simulations and the important nature of the considered model,with the help of obtained results,shows the efficiency of the considered fractional operator and algorithm,while examining the nonlinear equations describing real-world problems.

关键词： Laplace transform Camassa–Holm equation q-homotopy analysis method Degasperis–Procesi equation fractional derivative

Solution for fractional potential KdV and Benjamin equations using the novel technique

维普期刊数据库

同方期刊数据库评论

在线全文

学校读者我要写书评

暂无评论

Journal of Ocean Engineering and Science 2021年第3期6卷 265-275页

作者： P.Veeresha D.G.Prakasha N.Magesh A.John Christopher Deepak Umrao Sarwe Department of Mathematics CHRIST(Deemed to be University)Bengaluru-560029India Department of Mathematics Faculty of ScienceDavangere UniversityShivagangothriDavangere-577007India P.G.and Research Department of Mathematics Govt.Arts College for MenKrishnagiri-635001India Department of Mathematics University of MumbaiKalinaSantacruz EastMumbai-400098India

In this paper,we find the solutions for fractional potential Korteweg-de Vries(p-KdV)and Benjamin equations using q-homotopy analysis transform method(q-HATM).The considered method is the mixture of q-homotopy analysis method and Laplace transform,and the Caputo fractional operator is considered in the present investigation.The projected solution procedure manipulates and controls the obtained results in a large admissible domain.Further,it offers a simple algorithm to adjust the convergence province of the obtained solution.To validate the q-HATM is accurate and reliable,the numerical simulations have been conducted for both equations and the outcomes are revealed through the plots and tables.Comparison between the obtained solutions with the exact solutions exhibits that,the considered method is efficient and effective in solving nonlinear problems associated with science and technology.

关键词： Potential KdV equation q-homotopy analysis method Fractional Benjamin equation Laplace transform Ginzburg-Landau equation Caputo fractional operator

analysis of Lakes pollution model with Mittag-Leffler kernel

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Ocean Engineering and Science 2020年第4期5卷 310-322页

作者： D.G.Prakasha P.Veeresha Department of Mathematics Faculty of ScienceDavangere UniversityShivagangothriDavangere-577007KarnatakaIndia Department of Mathematics Karnatak UniversityDharwad-580003KarnatakaIndia

The pivotal aim of the present investigation is to find an approximate analytical solution for the system of three fractional differential equations describing the Lakes pollution using q-homotopy analysis transform method(q-HATM).We consider three different cases of the considered model namely,periodic input model,exponentially decaying input model,and linear input model.The considered scheme is unifications of q-homotopy analysis technique with Laplace transform(LT).To illustrate the existence and uniqueness for the projected model,we consider the fixed point hypothesis.More preciously,we scrutinized the behaviour of the obtained solution for the considered model with fractional-order,in order to elucidate the effectiveness of the proposed algorithm.Further,for the different fractional-order and parameters offered by the considered method,the physical natures have been apprehended.The obtained consequences evidence that the proposed method is very effective and highly methodical to study and examine the nature and its corresponding consequences of the system of fractional order differential equations describing the real word problems.

关键词： Lakes system Atangana-Baleanu derivative Laplace transform Fixed point theorem q-homotopy analysis method

An efficient computational technique for time-fractional modified Degasperis-Procesi equation arising in propagation of nonlinear dispersive waves

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Journal of Ocean Engineering and Science 2021年第1期6卷 30-39页

作者： Ved Prakash Dubey Rajnesh Kumar Jagdev Singh Devendra Kumar Faculty of Mathematical and Statistical Sciences Shri Ramswaroop Memorial UniversityLucknow-Deva RoadUttar Pradesh-225003India Department of Applied Science and Humanities Government Engineering CollegeNawadaDepartment of Science and TechnologyBihar-805122India Department of Mathematics JECRC UniversityJaipur-303905RajasthanIndia Department of Mathematics University of RajasthanJaipur-302004RajasthanIndia

In this paper,an efficient hybrid numerical scheme which is based on a joint venture of the q-homotopy analysis method and Sumudu transform is applied to investigate the time-fractional modified Degasperis-Procesi(DP)equation.The present study considers the Caputo fractional derivative.The fractional order modified DP model is very important and plays a great role in study of ocean engineering and science.The proposed scheme provides a beautiful opportunity for proper selection of the auxiliary parameter h and the asymptotic parameterρ(≥1)to handle mainly the differential equations of nonlinear nature.The offered scheme produces the solution in the shape of a convergent series in a large admissible domain which is helpful to regulate the region of convergence of a series solution.The proposed work computes the approximate analytical solution of the fractional modified DP equation systematically and also presents graphically the variation of the obtained solution for diverse values of the fractional parameterβ.

关键词： Fractional Degasperis-Procesi equation Nonlinear dispersive waves Analytical solution q-homotopy analysis method Sumudu transform