Partial Differential Equations in Applied Mathematics最新文献

{"title":"The Modified Homogeneous Balance Method for solving fractional Cahn–Allen and equal width equations","authors":"Francis Tuffour,&nbsp;Benedict Barnes,&nbsp;Isaac Kwame Dontwi,&nbsp;Kwaku Forkuoh Darkwah","doi":"10.1016/j.padiff.2025.101246","DOIUrl":"10.1016/j.padiff.2025.101246","url":null,"abstract":"<div><div>This paper presents exact solutions to the Fractional Cahn–Allen (FC–A) and the Fractional Equal Width (FEW) equations using the Modified Homogeneous Balance Method (MHBM). The MHBM transforms the FC–A and FEW equations into fractional ordinary differential equations via a wave transformation. By balancing the highest-order derivative with the leading nonlinear term, the method determines the appropriate polynomial degree. A fractional Riccati equation with a quadratic nonlinearity facilitates the construction of exact solutions without resorting to infinite series expansions. Compared to existing methods, the MHBM offers a finite and well-defined solution structure, avoiding the rigidity of the <span><math><mrow><mo>tan</mo><mfenced><mrow><mfrac><mrow><mi>ξ</mi><mrow><mo>(</mo><mi>η</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfenced></mrow></math></span>-expansion method and the complexities associated with the Riemann–Hilbert and algebro–geometric methods. It also provides clearer criteria for convergence analysis than the <span><math><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>6</mn></mrow></msup></math></span>-expansion method. The MHBM accommodates various solution types, including trigonometric, hyperbolic, rational, and elliptic functions, with fewer parameter restrictions and potential for multi-wave structures. Numerical simulations shows that as the spatial variable <span><math><mi>x</mi></math></span> increases, the solitons tend to stabilize, and the plots for different values of the fractional order <span><math><mi>α</mi></math></span> closely aligned, indicating minor sensitivity to <span><math><mi>α</mi></math></span>. Furthermore, the FEW soliton exhibits a dense tiling structure along the time axis in its surface plot, while the FC–A soliton demonstrates a smooth kink-like transition along <span><math><mi>ξ</mi></math></span>, characteristic of solutions connecting two stable equilibrium states. These findings underscore the robustness and versatility of the MHBM in analyzing fractional nonlinear evolution equations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101246"},"PeriodicalIF":0.0,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144562991","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}

{"title":"Non-uniqueness of the solution of the Cauchy problem for one higher-order equation with a fractional derivative","authors":"B. Yu. Irgashev ,&nbsp;H.H. Pulatova","doi":"10.1016/j.padiff.2025.101252","DOIUrl":"10.1016/j.padiff.2025.101252","url":null,"abstract":"<div><div>In the article a non-trivial solution of the homogeneous Cauchy problem for a homogeneous high-order equation with a fractional Caputo derivative is constructed.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101252"},"PeriodicalIF":0.0,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571098","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}

{"title":"Thermal radiation effect on fractional MHD Couette Flow of Jeffrey fluid in a vertical channel with activation energy and Joule Heating","authors":"Paul M. Matao ,&nbsp;Jumanne Mng’ang’a ,&nbsp;B. Prabhakar Reddy","doi":"10.1016/j.padiff.2025.101251","DOIUrl":"10.1016/j.padiff.2025.101251","url":null,"abstract":"<div><div>This study investigates the consequence of thermal radiation on the fractional magnetohydrodynamic (MHD) Couette flow of a Jeffrey fluid in a vertical channel, incorporating the influences of activation energy and Joule heating. The mathematical model is derived using appropriate governing equations that account for the non-Newtonian behavior of the Jeffrey fluid, combined with the impacts of thermal radiation, magnetic field, and activation energy mechanisms. The classical mathematical framework has been transformed into a system of fractal fractional-order derivatives using the Caputo–Fabrizio derivative operator. To solve these systems, the finite difference technique was employed. The behavior of fluid flow fields in response to several significant parameters was analyzed and represented graphically. It is ascertained that velocity distribution upsurges as Hall current parameter rises, while a more substantial effect from the Jeffrey fluid parameter results in a decrease in the velocity field. Additionally, thermal field profiles exhibited higher values in response to increased thermal radiation and Joule heating parameters, whereas the temperature distribution showed a decline with improving in Hall current parameter values. The concentration field improved with higher activation energy parameter values, in contrast to the opposite trend observed with temperature difference and chemical reaction parameters. Furthermore, it is remarked that fractal fractional-order derivatives operator produced a more pronounced boundary layer compared to both fractional and classical models. It is ascertained that the Nusselt number showing a 15.7% improvement in thermal efficiency as thermal radiation varied from 2 to 4. These findings are important for applications in geothermal energy extraction, and biomedical engineering.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101251"},"PeriodicalIF":0.0,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144557626","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}

{"title":"Analytical new soliton solutions and stability analysis of the (2 + 1)-dimensional time-fractional nonlinear GZKBBM equation","authors":"Nazia Parvin ,&nbsp;Hasibun Naher ,&nbsp;M. Ali Akbar","doi":"10.1016/j.padiff.2025.101256","DOIUrl":"10.1016/j.padiff.2025.101256","url":null,"abstract":"<div><div>In this study, we investigate the soliton solutions of the (2 + 1)-dimensional time-fractional nonlinear generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation using the extended sinh-Gordon expansion approach. This equation is useful in modeling the hydro-magnetic waves in cold plasma, acoustic waves in harmonic crystals, shallow water waves, and acoustic gravity waves. By utilizing the suggested approach, we derive some rich structured soliton solutions, including bell-shaped soliton, anti-bell-shaped soliton, anti-peakon, periodic soliton and singular solitons of the model. These solutions are expressed in hyperbolic and trigonometric forms, and their dynamical behaviors are illustrated through 3D and 2D plots for various values of the fractional parameter <span><math><mrow><mi>β</mi><mspace></mspace></mrow></math></span>and other physical parameters. The impact of the time-fractional derivative on the introduced model is examined using the beta derivative framework, which provides a more general and flexible way to enhance the accuracy of the solutions. The stability of the model is also examined through the linear stability theory, confirming that all analytical findings are stable. The results unambiguously demonstrate that the extended sinh-Gordon expansion approach is compatible, reliable, and efficient for investigating various nonlinear evolution equations in fields of applied science and engineering.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101256"},"PeriodicalIF":0.0,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571611","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}

{"title":"Numerical approximation of time-fractional nonlinear partial integro-differential equation using fractional Euler and cubic trigonometric B-Spline methods","authors":"Mehwish Saleem ,&nbsp;Arshed Ali ,&nbsp;Fazal-i-Haq ,&nbsp;Hassan Khan","doi":"10.1016/j.padiff.2025.101223","DOIUrl":"10.1016/j.padiff.2025.101223","url":null,"abstract":"<div><div>Nonlinear mathematical problems arise due to existence of important complex nonlinear phenomena in engineering and science. In this article, a class of time-fractional nonlinear parabolic partial integro-differential equations is solved numerically by combination of fractional Euler and cubic trigonometric B-spline collocation methods. Backward finite difference formula is employed for time-fractional Caputo derivative to get an unconditional stable scheme. The memory(integral) term is evaluated using a second order quadrature rule. Fractional Euler method for Caputo derivative is used in computing the nonlinear memory term. At each time level, cubic trigonometric B-spline functions are applied to obtain the solution in spatial dimension which reduces the problem to a system of algebraic equations. This method has the ability to handle any kind of nonlinearity without using iterative processes. Efficiency and reliability of the current method is analyzed for the fractional-order via three highly nonlinear test problems with variable coefficients. The rate of convergence of the proposed method is also computed in temporal and spatial dimensions.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101223"},"PeriodicalIF":0.0,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144672280","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}

{"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":"2025-06-30","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}

{"title":"Analysis of fractional viewpoints on the Jaulent–Miodek and Whitham–Broer–Kaup coupled equations","authors":"Sachit Kumar ,&nbsp;Varun Joshi ,&nbsp;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":"2025-06-27","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}

{"title":"Mathematical model of Cynodon Dactylon’s allelopathic effect on perennial ryegrass for exploring plant-plant interactions based upon ordinary differential equations","authors":"Dipesh ,&nbsp;Pankaj kumar ,&nbsp;Anjori Sharma","doi":"10.1016/j.padiff.2025.101254","DOIUrl":"10.1016/j.padiff.2025.101254","url":null,"abstract":"<div><div>In this paper, a mathematical model and analysis is proposed to study the stimulatory allelopathic impact of cynodon dactylon on perennial ryegrass using ordinary differential equations. Equilibrium points and biological interpretation is analyzed using the Routh-Hurwitz theorem. Allelopathic produces synergistic effects between two plants that can result in apparent competition for space, nutrients, water and growth of the plant or apparent organisms depending on how the life cycles of their shared exploiters and/or commensal are influenced by inducing morphological, physiological, biochemical and chemical changes in plants. Plants are competing for space, which is required for proper growth and development of roots. Based on spacing allelopathic effect is very less as space increases in respect of root length and root branches increase. These allelopathy biochemicals are used for pest management. Whenever the behaviors of exploiters and commensals respond to induce changes in comparative plant numbers, indirect -interactions among plants arise<strong>.</strong> The Mann-Kendall, MK test, Bartletts test, and Anova test is used to analyze the data and numerical simulation. Also, the main objective of this research article allelopathic impact of plant-to-plant interaction research plays an important role in climate action and life cycle on land.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101254"},"PeriodicalIF":0.0,"publicationDate":"2025-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144548425","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}

{"title":"The impact of carbon nanotubes (CNT) on heat generation and absorption, the behaviour of water and blood suspensions in an inclined channel with a porous matrix","authors":"Mangala Kandagal ,&nbsp;Ramesh Kempepatil ,&nbsp;Jagadish V. Tawade ,&nbsp;Nodira Nazarova ,&nbsp;Manish Gupta ,&nbsp;M. Khan","doi":"10.1016/j.padiff.2025.101241","DOIUrl":"10.1016/j.padiff.2025.101241","url":null,"abstract":"<div><div>The study investigates the heat generation and absorption of engine oil, human blood and single wall carbon Nano tube (SWCNT) in an inclined channel filled with a porous matrix. Two regions are considered, both regions are of porous medium. Due to their enhanced thermal conductivity, are utilized to improve heat transfer efficiency in various applications. Formulation of the problem is framed using conservation of mass, energy and momentum in both regions. The flow of oil, human blood through a porous medium is analysed, considering the effects of both heat generation and absorption within the system. Key parameters such as the inclination angle of the channel, the porosity and the type of fluids are examined to understand their impact on the overall heat transfer process and velocity. To solve the problem regular perturbation method is applied for non-dimensional quantities; The presence of CNTs significantly improves the thermal conductivity of both engine oil and blood suspensions, leading to improved heat dissipation or absorption capabilities, which are influenced by the inclination and the porous structure. This study offers valuable insights into fluid flow processes in the human body using Nanotubes. Influence of CNTs on the fluid flow of human body and heat generation/absorption with porous matrix in both regions is unsolved problem.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101241"},"PeriodicalIF":0.0,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144571613","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}

{"title":"Detailed analysis under fully constrained and relaxed boundary conditions of linear fields in the vicinity of a corner","authors":"Ayelet Goldstein,&nbsp;Ofer Eyal,&nbsp;Jorge Berger","doi":"10.1016/j.padiff.2025.101244","DOIUrl":"10.1016/j.padiff.2025.101244","url":null,"abstract":"<div><div>This work examines the behavior of fields near corners under various boundary conditions (BCs), focusing on singularities arising from fully constrained and relaxed BCs. We analyze this behavior across diverse physical systems governed by similar equations, including electromagnetism, superconductivity, and two-phase fluid flow. The corner geometry presents a challenge due to potentially diverging field solutions as the corner is approached (r<span><math><mo>→</mo></math></span> 0). This motivates the investigation of relaxed BCs, which regularize the field by introducing a characteristic length (Ls) that relates the field’s value to its normal derivative at the boundary.</div><div>We explore both single-medium (single-phase) and double-medium (two-phase) systems. While prior research has addressed relaxed BCs in specific contexts, their application to corners, particularly in diverse physical systems, remains under-explored. We develop a series solution method to analyze the field behavior near the corner under different BCs. Concrete examples illustrate the theoretical framework, examining both fully constrained and relaxed scenarios. The implications of this work extend to fields such as fluid mechanics, electromagnetism, and heat transfer.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101244"},"PeriodicalIF":0.0,"publicationDate":"2025-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144557625","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}