Partial Differential Equations in Applied Mathematics最新文献

{"title":"Analytical simulation of the nonlinear Caputo fractional equations","authors":"Ali Ahadi ,&nbsp;Seyed Mostafa Mousavi ,&nbsp;Amir Mohammad Alinia ,&nbsp;Hossein Khademi","doi":"10.1016/j.padiff.2025.101264","DOIUrl":"10.1016/j.padiff.2025.101264","url":null,"abstract":"<div><div>Partial differential equations (PDEs), particularly those involving fractional derivatives, have garnered considerable attention due to their ability to model complex systems with memory and hereditary properties. This paper focuses on the generalized Caputo fractional equation and presents a comparative analysis of three powerful solution techniques: the Homotopy Perturbation Method (HPM), the Variational Iteration Method (VIM), and the Akbari-Ganji Method (AGM). These methods are applied to fractional differential equations (FDEs) to derive approximate solutions. The accuracy and effectiveness of the methods are demonstrated through detailed comparisons with exact solutions and previous works in the field.</div><div>The study highlights the strengths of each technique in handling non-linear and fractional-order problems, providing reliable results with minimal error. Specifically, the HPM and VIM show remarkable convergence properties, while the AGM proves efficient in solving both linear and non-linear equations. These methods are validated by comparing the results with known solutions, which shows that these techniques work for a wide range of FDEs. The present study underscores the applicability of these approaches in several scientific and technological domains, hence promoting more advancements in the numerical examination of fractional systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101264"},"PeriodicalIF":0.0,"publicationDate":"2025-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724410","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":"Data analysis of entropy generation in quadratic radiative with chemically reactive Williamson fluid flow past an inclined porous sheet","authors":"Md. Yousuf Ali,&nbsp;Mizanur Rahman,&nbsp;Md. Shakib Hossain,&nbsp;Mst. Sharmin Akter,&nbsp;Noor Muhammad,&nbsp;Atia Sanjida Talukder","doi":"10.1016/j.padiff.2025.101266","DOIUrl":"10.1016/j.padiff.2025.101266","url":null,"abstract":"<div><div>Data analysis (DA) is crucial in materials science and engineering for optimizing heat and mass transport processes. This study investigates the impact of magneto-hydrodynamics (MHD), quadratic radiation, and chemical reactions on entropy generation in Williamson fluid over an inclined porous sheet (IPS). It uses a numerical approach that integrates the 6th-order Runge-Kutta (R-K) method with the Nachtsheim-Swigert (N-S) shooting technique after transforming the governing equations into ordinary differential equations (ODEs). The research aims to elucidate the entropy generation dynamics of the Williamson fluid, examining the effects of quadratic radiative MHD chemical reactions. The key novelty of this work is that for 0.5 ≤ <em>Kr</em> ≤ 2.5, entropy production increases by 90.09% with linear radiation and by 114.60% with quadratic radiation, with the increase being higher for quadratic radiation. However, entropy generation for quadratic radiation is 14.10% lower than for linear radiation at <em>Kr</em> = 0.5. For an inclined sheet, it is 8.14% less than for a flat sheet at <em>K</em> = 2.5, and for Williamson fluid, it is 3.76% less than for Newtonian fluid at a diffusion coefficient of <em>ϑ</em> = 1.0. Additionally, the temperature increases in both the linear as well as quadratic radiation situations when the Williamson and radiation parameters increase. Regression analysis confirms the model's durability and accuracy at a 95% confidence level, with an <em>R</em>² value of 99.92% and a strong positive correlation of over 99% between chemical processes and entropy creation. Understanding entropy production is crucial for optimizing cooling systems and heat exchangers, including biotechnology.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101266"},"PeriodicalIF":0.0,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724411","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 MHD radiative flow of ternary hybrid nanofluid over a porous stretching surface","authors":"Shital Sobale ,&nbsp;Jagadish V. Tawade ,&nbsp;Pooja Bagane ,&nbsp;Vediyappn Govindan ,&nbsp;Barno Abdullaeva ,&nbsp;Hawzhen Fateh M. Ameen ,&nbsp;Manish Gupta ,&nbsp;Nadia Batool","doi":"10.1016/j.padiff.2025.101267","DOIUrl":"10.1016/j.padiff.2025.101267","url":null,"abstract":"<div><div>The present work focuses on the exploration of MHD ternary hybrid nanofluid (THNF) flow of boundary layer past a porous stretching surface. In this investigation, we have analysed how various sources such as magnetic field, porosity, heat generation, radiation affect the flow dynamics. The novelty of the work is to understand the heat transfer phenomenon of <span><math><mrow><mi>A</mi><msub><mi>l</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub><mo>,</mo><mo>−</mo><mi>T</mi><mi>i</mi><msub><mi>O</mi><mn>2</mn></msub><mo>−</mo><mi>A</mi><mi>g</mi><mo>/</mo><mi>w</mi><mi>a</mi><mi>t</mi><mi>e</mi><mi>r</mi></mrow></math></span> hybrid nanofluid subjected to magnetic field, viscous dissipation, radiation and porosity effects. of To understand the flow behaviour better associated partial differential equations were transformed to ordinary differential equations via similarity transformations. We have explored this resulting system through MATLAB bvp4c. The results showed that thermal radiation, solid volume fraction improved heat transfer in THNFs as compared to HNFs. By varying the values of various parameters of flow like solid volume fraction, magnetic field parameter, radiation parameter, permeability parameter we have thoroughly studied and compared the flow dynamics with the previously established results. The study has real world applications involving solar plants, applications demanding improved heat transfer and energy saving applications such as air coolers etc.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101267"},"PeriodicalIF":0.0,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144724517","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":"Influence of heat source on Casson nanofluid flow over an exponentially stretching sheet","authors":"Sangamesh ,&nbsp;K.R. Raghunatha ,&nbsp;Ali J. Chamkha ,&nbsp;Vinod Y","doi":"10.1016/j.padiff.2025.101262","DOIUrl":"10.1016/j.padiff.2025.101262","url":null,"abstract":"<div><div>The research examines the behaviour of nanofluid flow, incorporating Casson fluid properties and a heat source, as it moves over a sheet that stretches exponentially at the stagnation point. The interplay of Brownian motion and thermophoretic properties adds to the complexity, creating a coupled nonlinear boundary-value problem (BVP). The original partial differential equations (PDEs) are converted into ordinary forms by applying proper similarity conversions. Initially formulated for an infinite domain [0, ∞), the problem was then converted to a finite domain [0, 1] using wavelet transformations. The Bernoulli wavelet method (BWM) was employed to numerically solve the transformed equations within the MATHEMATICA 12 platform. The obtained findings are extremely compared with earlier research that examined various specific scenarios within the problem. A detailed investigation of the physical limitations is conducted and the numerical results are visually presented to provide clear illustrations. A higher Prandtl number leads to reduced thermal diffusivity, resulting in a thinner thermal boundary layer and steeper temperature gradients concentrated near the surface. Similarly, an increase in the Lewis number lowers molecular diffusivity, producing a more confined solutal boundary layer. The presence of an internal heat source further elevates fluid temperature near the stretching sheet, expanding the thermal boundary layer due to added thermal energy.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101262"},"PeriodicalIF":0.0,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144704591","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":"Fractional order modeling of prophylactic measures on the transmission dynamics of measles: An optimal control analysis","authors":"Adedapo Chris Loyinmi ,&nbsp;Alani Lateef Ijaola","doi":"10.1016/j.padiff.2025.101259","DOIUrl":"10.1016/j.padiff.2025.101259","url":null,"abstract":"<div><div>In this study, we presented a fractional order transmission model to investigate the dynamics and potential controls for measles, in order to accurately represent the dynamics of its transmission. We propose a modified S, V, E, I and R (Susceptible, Vaccinated, Exposed, Infectious and Recovered individuals), a workable human population model with an incident rate equipped with a saturation factor to investigate the combined impact of three prophylactic techniques, which are public awareness, second dose vaccination and proper treatment in case of severity.. Here, we assumed there is a vaccinated population that has taken first dose in the proposed model. We established among other things, the parameter responsible for invasion, the reproductive number,<em>R</em>₀ is less than unity through the stability analysis and the numerical solution of the fractional order model was done using the Adams Bashforth predictor-corrector method. In addition, the effects of the prophylactic measures and the fractional order (α) were simulated and findings from the graphical solutions depict that these measures aid in flattening out the trajectory of the disease if measure are properly implemented.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101259"},"PeriodicalIF":0.0,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680601","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":"Exploration of the Arrhenius activation energy in unsteady ternary hybrid nanofluid flow past a slendering stretching sheet: RSM analysis","authors":"N. Nithya ,&nbsp;B. Vennila ,&nbsp;K. Loganathan ,&nbsp;R. Shobika ,&nbsp;K. Senthilvadivu ,&nbsp;S. Eswaramoorthi","doi":"10.1016/j.padiff.2025.101255","DOIUrl":"10.1016/j.padiff.2025.101255","url":null,"abstract":"<div><div>This paper examines how a ternary hybrid nanofluid made by combining <span><math><msub><mrow><mtext>TiO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>, <span><math><msub><mrow><mtext>SiO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>, and <span><math><mrow><msub><mrow><mtext>Al</mtext></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mtext>O</mtext></mrow><mrow><mn>3</mn></mrow></msub></mrow></math></span> in water behaves when flowing across a stretching sheet with varying thickness. The motivation comes from real world needs in systems like solar collectors, biomedical devices, and industrial cooling, where better heat transfer with minimal drag is essential. Using a blend of the Differential Transformation Method (DTM) and statistical optimization techniques like Response Surface Methodology (RSM) and Central Composite Design (CCD), we study how magnetic field, radiation, nanoparticle volume fraction, and activation energy affects the system. The hybrid nanofluid’s improved thermal behavior is a key focus. It is found that the increasing sheet thickness leads to higher temperatures, while velocity and concentration drop. Greater thermal radiation and more silicon dioxide particles enhance the heat transfer, improving efficiency by 12% and reducing drag (skin friction) by 15% under optimized conditions. Thermal conductivity improves with more nanoparticles, raising the Nusselt number. Meanwhile, mass diffusion behavior captured by the Sherwood number is influenced by activation energy and the Schmidt number. Magnetic field and nanoparticle volume fraction effects together help lower surface drag.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101255"},"PeriodicalIF":0.0,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680602","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":"Exact solution of system of nonlinear fractional partial differential equations by modified semi-separation of variables method","authors":"Henry Kwasi Asiedu,&nbsp;Benedict Barnes,&nbsp;Isaac Kwame Dontwi,&nbsp;Kwaku Forkuoh Darkwah","doi":"10.1016/j.padiff.2025.101247","DOIUrl":"10.1016/j.padiff.2025.101247","url":null,"abstract":"<div><div>A system of nonlinear fractional partial differential equations (FPDEs) is widely used in applied sciences, especially for modeling fluid dynamics and polymer-related problems. Given their importance, finding solutions to these systems is essential and a core property. Various methods have been developed to find a solution to a system of nonlinear FPDEs. However, these methods are difficult to implement and sometimes converge slowly. In the worst-case scenario, applying the differential transform method may produce a series that does not converge to the exact solution of a system of nonlinear FPDEs. The semi-separation of variables method (S-SVM) is a recent and reliable analytic method that has not been applied to obtain an exact solution to a system of nonlinear FPDEs. Furthermore, S-SVM has not been improved to observe faster convergence. In this paper, the S-SVM is used to obtain the exact solution to the system of nonlinear FPDEs. In addition, the S-SVM is further improved as a Modified S-SVM (MS-SVM), which is applied to find an exact solution to the system of nonlinear FPDEs. Also, numerical experiments using the S-SVM and the MS-SVM in both two and three dimensions are provided therein, along with a comparison of their solutions to those obtained from the Adomian Decomposition Method (ADM), the Laplace Variational Iteration Method (LVIM), and the Fractional Power Series Method (FPSM). The results show that the solutions obtained using S-SVM and MS-SVM converge faster than those from FPSM, ADM, and LVIM. Moreover, S-SVM and MS-SVM do not require the complex computation of Adomian polynomials.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101247"},"PeriodicalIF":0.0,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144656868","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":"An immersed interface method for nonlinear convection–diffusion equations with interfaces","authors":"Miguel Uh Zapata ,&nbsp;Reymundo Itza Balam ,&nbsp;Silvia Jerez","doi":"10.1016/j.padiff.2025.101250","DOIUrl":"10.1016/j.padiff.2025.101250","url":null,"abstract":"<div><div>This paper provides an initial framework for developing high-order numerical methods to solve interface problems for nonlinear elliptic partial differential equations. The proposed formulation is based on the immersed interface method dealing with a discontinuous coefficient problem. The algorithm introduces new schemes for points near the interface, whereas standard central finite difference schemes are used in smooth regions. As a consequence, a global second-order accurate solution is guaranteed. First, theoretical results on the truncation error are given for one-dimensional linear problems. Next, the algorithm is generalized to deal with nonlinear convection and diffusion cases using the using Levenberg–Marquardt algorithm. Numerical simulations for several benchmark problems show the robustness and efficiency of the proposed scheme.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101250"},"PeriodicalIF":0.0,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614845","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":"Qualitative analysis and controllability of complex tumor model with different therapies with nonsingular kernel","authors":"Maryam Batool ,&nbsp;Muhammad Farman ,&nbsp;Kottakkaran Sooppy Nisar ,&nbsp;Evren Hincal ,&nbsp;Shah Jahan","doi":"10.1016/j.padiff.2025.101249","DOIUrl":"10.1016/j.padiff.2025.101249","url":null,"abstract":"<div><div>In this paper, consider the immune response to avascular cancer under the effect of immunotherapy, chemotherapy, and their combinations, as well as vaccination regimens, is described using a fractional order model to observe the impact of different therapies for cancer treatment. The impact of vaccination therapy is viewed as a model parameter perturbation. The effect of the global derivative, the existence, and the boundedness of the suggested system are confirmed, which are the essential characteristics of epidemic problems. The proposed system is qualitatively examined as well to determine its stable points. The Lyapunov function is used to analyze global stability, and the equilibrium states of the second derivative test are quantitatively examined. To investigate the effects of the fractional operator on the suggested model, solutions are generated using the Mittag Leffler kernel, and numerical simulations are run to demonstrate the theoretical findings. Using MATLAB, the effects of cancer treatment with various drugs and parameter values are justified. The proposed system is also treated for controllability and observability for a linear control system to monitor the close-loop design with different therapies as an input and cancer cells as an output.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"15 ","pages":"Article 101249"},"PeriodicalIF":0.0,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144656869","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 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}