Partial Differential Equations in Applied Mathematics最新文献_第9页

Optical soliton solutions of M-fractional modified complex Ginzburg-Landau equation using unified method: A comparative study m分数阶修正复金兹堡-朗道方程光学孤子统一解的比较研究

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-06-15 DOI: 10.1016/j.padiff.2025.101245

Md. Mamunur Roshid, Sayma Akter, Bithi Akter

{"title":"Optical soliton solutions of M-fractional modified complex Ginzburg-Landau equation using unified method: A comparative study","authors":"Md. Mamunur Roshid, Sayma Akter, Bithi Akter","doi":"10.1016/j.padiff.2025.101245","DOIUrl":"10.1016/j.padiff.2025.101245","url":null,"abstract":"<div><div>The current research investigates the M-fractional modified complex Ginzburg-Landau equation, a crucial nonlinear model for characterizing the behavior and evolution of optical solitary waves in dynamic fiber optics. Examining wave propagation in nonlinear dispersive media is essential since it promotes progress in data transmission for communication systems and allows for generating ultrafast optical pulses. the M-fractional derivative for the MCGL model is applied for the first time, which is more meaningful. The equation is converted into an ordinary differential equation via wave transformation, enabling the use of a unified technique to get many soliton solutions. By applying the unified method, we obtain more solutions than other methods, such as the function transformation technique.<sup>23</sup> The solutions are expressed as <em>tanh</em>, <em>sec</em>, <em>tan</em>, <em>sech</em> functions and their combinations. For the special values of free parameters, we have periodic waves, kinky-periodic waves, periodic lump waves, periodic waves with lump waves, interactions of anti-kink and periodic waves, double periodic waves, and multi-kink waves. This work's innovative component is applying this approach to derive various soliton structures, analyzed using 2D, 3D, and contour representations. Additionally, the influence of fractional parameter presents with 3D plots for γ = 0.1, 0.4, 0.8. we also compare the fractional effect with the classical form in 2D plots. The results highlight the efficacy of this approach in examining soliton solutions in diverse nonlinear models, hence enhancing the comprehension of wave dynamics in mediums with differing stability.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101245"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Statistical and numerical investigation of irreversibility for time-dependent Casson-Carreau nanofluid flow driven by curved surface: Regression analysis 曲面驱动下随时间卡森-卡罗纳米流体不可逆性的统计和数值研究：回归分析

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-07-25 DOI: 10.1016/j.padiff.2025.101263

P. Kumar , AR. Ajaykumar , F. Almeida , S. Saranya , Qasem Al-Mdallal

{"title":"Statistical and numerical investigation of irreversibility for time-dependent Casson-Carreau nanofluid flow driven by curved surface: Regression analysis","authors":"P. Kumar , AR. Ajaykumar , F. Almeida , S. Saranya , Qasem Al-Mdallal","doi":"10.1016/j.padiff.2025.101263","DOIUrl":"10.1016/j.padiff.2025.101263","url":null,"abstract":"<div><div>Statistical and numerical approach is provided in the current article for Casson-Carreau nanofluid transient flow over continuously elongated sheet of curved feature. The flow is subjected under the various generation, Joule heating, non-linear thermal radiation, activation energy, second order slip, and convective peripheral conditions. Identifying the parameters that optimize the heat transfer rate and using those parameters applying the appropriate statistical tool to optimize the heat transfer rate are the two motives behind this study. A regression analysis is executed on the entropy generated; it has analyzed statistically using response surface methodology. For the issue under consideration, a Runge-Kutta-Fehlberg 4–5th order scheme has been implemented. Here, the study shows that although the Darcy number and first order slip decelerates velocity, the second order slip improves the velocity regime. Additionally, the study has showed that the activation energy parameter leverages the same, while chemical reaction parameter has negative effect on mass dispersion. With an increase in Brinkmann number, entropy production likewise rises, and fluid friction irreversibilities become more prevalent. As unsteadiness and activation energy parameters increase, Sherwood number declines. The visual representation of isotherms and streamlines is presented to display the flow and temperature pattern as a summary of the study. For the experimental setup by RSM, the better correlation coefficient is 99.93 % attained. The Pareto-chart specifies 2.2 to be the vital point for the statistical experimental design considered. For all the levels of heat source parameter and Eckert number, Radiation parameter exhibits positive sensitivity.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101263"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144829639","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Investigating traveling wave structures in the van der Waals normal form for fluidized granular matter through the modified S-expansion method 用改进的s -膨胀法研究流化颗粒物质范德华范式的行波结构

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-08-23 DOI: 10.1016/j.padiff.2025.101285

Hamida Parvin , Md. Nur Alam , Md. Abdullah Bin Masud , Md. Jakir Hossen

{"title":"Investigating traveling wave structures in the van der Waals normal form for fluidized granular matter through the modified S-expansion method","authors":"Hamida Parvin , Md. Nur Alam , Md. Abdullah Bin Masud , Md. Jakir Hossen","doi":"10.1016/j.padiff.2025.101285","DOIUrl":"10.1016/j.padiff.2025.101285","url":null,"abstract":"<div><div>This research discovers traveling wave solutions (TWSs) of the van der Waals normal form for fluidized granular matter using the modified S-expansion (MS-E) method. The model captures key behaviors such as phase transitions, clustering, and shock structures in granular flows. Applying a traveling wave transformation reduces the governing equation to a nonlinear ordinary differential equation (NODE), enabling the construction of TWSs relevant to geophysical and industrial applications. The MS-E technique is implemented to systematically derive TWSs—such as kink, bright, and dark solitons—that model density waves, shock fronts, and clustering in granular media. Comprehensive 2D, 3D, and contour plots are presented to validate and visualize the results, offering insights into wave behavior and soliton stability. This work highlights the MS-E method as a powerful tool for solving nonlinear integral and fractional partial differential equations (NLIFPDEs), with broad applications in granular physics, fluid mechanics, plasma waves, and nonlinear optics. This experiment offers a novel procedure to explore additional compound nonlinear wave phenomena by integrating the MS-E method, opening novel opportunities for additional expansions in soliton-driven knowledge. This method offers a promising pathway for future researchers to explore closed-form traveling wave solutions of other NLIFPDEs.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101285"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145018631","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Analysis of fractional viewpoints on the Jaulent–Miodek and Whitham–Broer–Kaup coupled equations Jaulent-Miodek和Whitham-Broer-Kaup耦合方程的分数视点分析

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-06-27 DOI: 10.1016/j.padiff.2025.101243

Sachit Kumar , Varun Joshi , Mamta Kapoor

{"title":"Analysis of fractional viewpoints on the Jaulent–Miodek and Whitham–Broer–Kaup coupled equations","authors":"Sachit Kumar , Varun Joshi , Mamta Kapoor","doi":"10.1016/j.padiff.2025.101243","DOIUrl":"10.1016/j.padiff.2025.101243","url":null,"abstract":"<div><div>In this work, we use the Caputo fractional calculus to methodically examine the Coupled Jaulent–Miodek (CJM) fractional equation and the fractional Whitham–Broer–Kaup (WBK) system. The Sumudu residual power series approach and the Sumudu iteration transform method are used to analyze the nonlinear fractional differential equation systems, providing a comprehensive analytical analysis. The Sumudu iteration transform approach is used to achieve the fractional WBK system’s dynamics, as well as the Sumudu power series residual approach is utilized to investigate the CJM equation’s behavior for fractions. We thoroughly examine their interactions using known solutions, using both symbolic calculations and numerical simulations. This leads to the identification of new solutions and the clarification of the way in which certain systems of fractions behave in terms of the operator of Caputo. The outcomes demonstrate the efficacy of the strategies used to decipher the intricate dynamics of fractional nonlinear systems by demonstrating a strong convergence agreement between analytical and numerical solutions.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101243"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144562992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A comparative analysis using the Laplace transform approach for some nonlinear fractional physical problems 用拉普拉斯变换方法对若干非线性分数物理问题的比较分析

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-06-30 DOI: 10.1016/j.padiff.2025.101253

Mohammad Alaroud

{"title":"A comparative analysis using the Laplace transform approach for some nonlinear fractional physical problems","authors":"Mohammad Alaroud","doi":"10.1016/j.padiff.2025.101253","DOIUrl":"10.1016/j.padiff.2025.101253","url":null,"abstract":"<div><div>Both linear and nonlinear differential, partial equations of fractional order can be solved efficiently using the residual power series method (RPSM). Nevertheless, the process requires the residual function's (<em>n</em> − 1)ϱ fractional derivative(FD). We all know that figuring out the FD of a function can be difficult. A straightforward and effective analytical technique known as the Laplace transform-residual power series method (LT-RPSM) is used in this study to provide the approximate and exact solutions to nonlinear fractional partial differential equations(NFPDEs) under Caputo fractional differentiation including the nonlinear Fokker-Planck, nonlinear gas dynamics and nonlinear Klein-Gordon equations. The computations needed to find the coefficients of an expansion series are modest because the proposed method just requires the concept of an infinite limit. Three nonlinear fractional physical problems are successfully solved by the used investigation, which provides closed- form solutions and exact solutions in ordinary case, also a thorough graphical and numerical comparisons of the findings discovered. These outcomes are compared with existing solutions in the literature, especially in the meaning of absolute errors against the Laplace Adomin decompostion method LADM in light of different FD operators. Strong agreement between the results of the used method and several series solution techniques. Consequently, LT-RPSM can be considered a very successful technique and the most effective analytical algorithm to deal with numerous NFPDEs emerging in physics and engineering.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101253"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144548424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Uniform indirect boundary observability for a spatial discretization of strongly coupled wave equations 强耦合波动方程空间离散化的均匀间接边界可观测性

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-07-29 DOI: 10.1016/j.padiff.2025.101261

Abderrahim El Ayboudi , Radoine Belkanoufi , Abdelkarim Hajjaj

引用次数: 0

Mathematical analysis of novel soliton solutions of the space-time fractional Chen-Lee-Liu model in optical fibers communication systems 光纤通信系统中时空分数陈-李-刘模型新孤子解的数学分析

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-08-24 DOI: 10.1016/j.padiff.2025.101295

M. Nurul Islam , M. Al-Amin , M. Ali Akbar

{"title":"Mathematical analysis of novel soliton solutions of the space-time fractional Chen-Lee-Liu model in optical fibers communication systems","authors":"M. Nurul Islam , M. Al-Amin , M. Ali Akbar","doi":"10.1016/j.padiff.2025.101295","DOIUrl":"10.1016/j.padiff.2025.101295","url":null,"abstract":"<div><div>The space-time fractional Chen-Lee-Liu (CLL) model is a significant optical fiber model utilized to analyze the performance of communication systems in optical fibers. It studies numerous features that may have impacts on the data transmission rates and signal excellence in optical fibers networks, nonlinearity, and noise. By developing this model, the engineers and researchers can optimize the design and performance in optical fiber communication systems. The optical solitons pulses of the CLL model are the fundamental construction block of soliton transmission technology, the telecommunication sector, and data transfer of optical fiber. In this study, we establish the significant soliton solutions which can be functional in optics of the stated model through the beta derivative employing the generalized exponential rational function technique (GERFT) which are not been investigated in the recent literature. The numerical simulations of the establishing solitons illustrates the bell-shaped, periodic, and some other soliton-like feature sand the examined shapes show the structure and influence of the fractional parameters. The results of this study exhibits that the implemented technique is efficient, reliable, and capable of establishing solutions to other complex nonlinear models in optical fiber communication systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101295"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144996471","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Magnetically driven free convection of nanofluids in rectangular cavities: A FEM approach 矩形空腔中纳米流体的磁驱动自由对流：有限元方法

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-08-22 DOI: 10.1016/j.padiff.2025.101291

Pramod S , Sujatha N , Sreekala C. K , Hanumagowda B. N , Kiran S , Jagadish V. Tawade , Manish Gupta , Barno Abdullaeva , M. Ijaz Khan

{"title":"Magnetically driven free convection of nanofluids in rectangular cavities: A FEM approach","authors":"Pramod S , Sujatha N , Sreekala C. K , Hanumagowda B. N , Kiran S , Jagadish V. Tawade , Manish Gupta , Barno Abdullaeva , M. Ijaz Khan","doi":"10.1016/j.padiff.2025.101291","DOIUrl":"10.1016/j.padiff.2025.101291","url":null,"abstract":"<div><div>This research paper comprehensively investigates magnetohydrodynamic free convection in a ferrofluid-filled rectangular cavity. The researchers designed a rectangular cavity where the left vertical wall maintains a warmer temperature than the right, while the horizontal walls (top and bottom) are adiabatic. A uniform magnetic field is imposed horizontally along the positive <em>x-</em>axis. The main objective is to analyse the impacts of various parameters, such as Hartmann number (0 ≤ <em>Ha</em> ≤ 60), Rayleigh number (10<sup>3</sup> ≤ <em>Ra</em> ≤ 10<sup>6</sup>), and volume fraction (0 ≤ ϕ ≤ 0.04), on the heat transfer characteristics and fluid flow behavior within the enclosure. The governing equations are rigorously solved using the Galerkin finite element method. Quality plots like streamlines and isotherms and quantity plots like average Nusselt number (<em>Nu<sub>a</sub></em>) are presented to elucidate the underlying physics. The findings indicate that increasing Rayleigh numbers increases the convective flow, whereas increasing Hartmann numbers decreases the convective flow, promoting conduction as the primary mode of heat transfer. It is also notable that the inclusion of a magnetic field significantly alters the flow and temperature distributions, leading to a notable reduction in average Nusselt number. Furthermore, the incorporation of nanoparticles is found to intensify the heat transfer rates, with higher volume fractions yielding greater thermal performance. These findings offer significant implications for advancing thermal management, material processing techniques, and magnetohydrodynamic power generation, thereby providing innovative heat transfer solutions across diverse engineering applications.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101291"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144902467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Fractional modelling of heat transfer through porous media for incompressible MHD fluid flow with laplace transform approach 用拉普拉斯变换方法模拟不可压缩MHD流体在多孔介质中的传热

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-06-18 DOI: 10.1016/j.padiff.2025.101242

Muhammad Kazim, Mubashir Abbas, Safder Hussain, Munawwar Ali Abbas

{"title":"Fractional modelling of heat transfer through porous media for incompressible MHD fluid flow with laplace transform approach","authors":"Muhammad Kazim, Mubashir Abbas, Safder Hussain, Munawwar Ali Abbas","doi":"10.1016/j.padiff.2025.101242","DOIUrl":"10.1016/j.padiff.2025.101242","url":null,"abstract":"<div><div>In this paper, we investigate a fractional model of an incompressible and unstable MHD viscous fluid with heat transfer pass across a porous medium. To quantify this, we used a vertical plate with a fluid connected to it. When an angled magnetic field is supplied, the plate moves in its own plane. The required nonlinear partial differential equations are used to convert the governing equations into a non-dimensional form. To find the solution of the simplified nonlinear partial differential equations, the Constant Proportional Caputo fractional derivatives are utilized. The Laplace transform techniques are used to simplify the non-dimensional governing equations of the model and the boundary conditions we discovered explicit formulations for each field. The resultant equation is solved for momentum and energy, and the solutions are given as series. The performance of velocity and temperature values are graphically plotted using MATHCAD software. In numerical simulation, the Local Skin fraction and local Nusselt number are considered and evaluated additionally. It has been concluded that the fluid’s temperature and velocity decreases by increasing the value of fractional parameter. It has also been found that the velocity and temperature increase with increasing values of<span><math><msub><mi>Q</mi><mn>0</mn></msub></math></span>.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101242"},"PeriodicalIF":0.0,"publicationDate":"2025-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144472180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Study on existence and stability analysis for implicit neutral fractional differential equations of ABC derivative 隐式中立型ABC导数分数阶微分方程的存在性及稳定性分析研究

Partial Differential Equations in Applied Mathematics Pub Date : 2025-09-01 Epub Date: 2025-08-29 DOI: 10.1016/j.padiff.2025.101276

V. Sowbakiya , R. Nirmalkumar , K. Loganathan , C. Selvamani

引用次数: 0