Partial Differential Equations in Applied Mathematics最新文献

{"title":"Integration of the fractional modified Korteweg de Vries-sine-Gordon equation with a variable time-dependent coefficients by the inverse scattering method","authors":"Bazar Babajanov,&nbsp;Fakhriddin Abdikarimov","doi":"10.1016/j.padiff.2026.101369","DOIUrl":"10.1016/j.padiff.2026.101369","url":null,"abstract":"<div><div>In this paper, we investigate the Cauchy problem for modified Korteweg de Vries-sine-Gordon equation with a Riesz fractional-order derivative containing time-dependent variable coefficients(vcRfmKdV-sG). We show that the inverse scattering transform(IST) method can also be used to obtain a soliton solutions of the vcRfmKdV-sG equation. We have determined the time evolution of the scattering data for the Ablowitz-Kaup-Newell-Segur system associated with the solution of the vcRfmKdV-sG equation. Then, using the solution of the inverse scattering problem with respect to the time-dependent scattering data, we recover the desired solution of the vcRfmKdV-sG equation. For the one- and two-soliton cases, explicit formulas for the solutions of the problem under consideration are derived as examples to simulate their spatial structures and analyze their structural properties by selecting different variable coefficients and fractional orders. The results indicate that both the variable coefficients and the fractional order significantly influence the velocity of soliton propagation, while no energy dissipation occurs throughout the entire motion process. This study contributes valuable insights into nonlinear dynamics and soliton behavior, improving the understanding of multifaceted wave interactions in nonlinear fractional equations.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"18 ","pages":"Article 101369"},"PeriodicalIF":0.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148230619","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":"Gravity-driven electromagnetic Casson nanofluid flow with Soret-Dufour and viscous heating effects over a porous slanted cone under non-uniform thermal source/sink: FDM approach","authors":"L. Joseph Sademaki ,&nbsp;B. Prabhakar Reddy ,&nbsp;J․ M. Sunzu","doi":"10.1016/j.padiff.2026.101370","DOIUrl":"10.1016/j.padiff.2026.101370","url":null,"abstract":"<div><div>This article evaluates the Soret-Dufour diffusion, Joule heating and heat-dissipation effects on two-dimensional unsteady gravity-driven electromagnetic flow of Casson nanofluids over a vertically slanted cone entrenched in a porous medium with variable thermal source/sink and higher-order chemical reactions. Specifically, two distinct nanofluids are synthesized by mixing two types <span><math><mtext>Ag</mtext></math></span> and <span><math><mtext>Cu</mtext></math></span> nanoparticles with the blend of water and ethylene-glycol as the base fluid. The explicit DuFort-Frankel finite difference scheme has been executed to discretize and solve the ultimate partial differential system. The research findings uncovered that the temperature field noticeably increased for both nanofluids by the Eckert parameter, radiation, Soret and Dufour impacts but it decays with nanoparticles capacity fraction. The Soret parameter and chemical reaction order elicited to expand concentration field for both nanofluids but chemical reaction and Schmidt number revealed opposite effect. Likewise, the velocity field lowered for both nanofluids by the cone’s inclination angle, magnetic intensity and Casson parameter whereas the porosity, radiation and Eckert number caused to inflate the velocity field for both nanofluids. The surface-friction improved for both nanofluids by the magnetic field, Casson and Dufour parameters but it was decayed by the nanoparticle’s concentration. An upsurge in magnetic field, thermal source and sink caused to downgrade Nusselt number for both nanofluids but the nanoparticle’s volume fraction exhibited opposite trend. The Sherwood number for both nanofluids enhanced with Schmidt number but it was decreased with chemical reaction and nanoparticles volume-fraction.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"18 ","pages":"Article 101370"},"PeriodicalIF":0.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148230620","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 investigation of using nano-encapsulated phase change materials for thermal energy storage","authors":"C Venkata Lakshmi ,&nbsp;Madapana Meena ,&nbsp;V Raja Rajeswari ,&nbsp;K Venkatadri","doi":"10.1016/j.padiff.2026.101371","DOIUrl":"10.1016/j.padiff.2026.101371","url":null,"abstract":"<div><div>This study presents a numerical investigation of free convection-driven melting of nano-encapsulated phase change material (NEPCM) within a semi-bottle-neck-shaped porous enclosure. The cavity is differentially heated, with the left vertical wall kept hot, the right wall kept cold, and the remaining walls adiabatic. The enthalpy–porosity method is employed to model the melting process, while the Darcy–Brinkman model governs flow within the porous matrix. Parametric analyses are performed across a range of Rayleigh numbers (Ra = 10³–10⁵), fusion temperatures (<span><math><msub><mi>θ</mi><mi>f</mi></msub></math></span> = 0.1–0.9), Stefan numbers (Ste = 0.1–0.9), nanoparticle volume fractions (ϕ = 0–0.05), Darcy numbers (Da = 10⁻⁴–10⁻¹), and Frank-Kamenetskii numbers (Fk = 0–1). Results reveal that increasing the nanoparticle volume fraction enhances thermal conductivity, leading to an improvement of up to 12.5% rise in the mean Nusselt number (<span><math><mrow><mi>N</mi><msub><mi>u</mi><mi>a</mi></msub></mrow></math></span>). A rise in fusion temperature <span><math><msub><mi>θ</mi><mi>f</mi></msub></math></span> from 0.1 to 0.9 leads to a 5.7% reduction in <span><math><mrow><mi>N</mi><msub><mi>u</mi><mi>a</mi></msub></mrow></math></span>. Stefan number increases from 0.2 to 0.7, producing a 9% decline in <span><math><mrow><mi>N</mi><msub><mi>u</mi><mi>a</mi></msub></mrow></math></span>, highlighting the latent heat damping effect. The Frank-Kamenetskii number, which characterizes internal heat generation due to exothermic reactions, significantly influences thermal transport: an increase in Fk from 0 to 1 decrease <span><math><mrow><mi>N</mi><msub><mi>u</mi><mi>a</mi></msub><mspace></mspace></mrow></math></span>by approximately 7.7%, indicating thermal thickening and slower melting fronts. Additionally, the semi-bottle-neck geometry intensifies localized circulation, while the application of a magnetic field attenuates convection, offering a controllable method to regulate thermal performance. These insights are vital in developing NEPCM-based phase change thermal energy storage systems in porous environments.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"18 ","pages":"Article 101371"},"PeriodicalIF":0.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148230621","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":"Temperature-dependent fluid properties on Ree-Eyring fluid flow through vertically oriented microchannel subject to rhythmic membrane contraction","authors":"M R Madhavi ,&nbsp;Manjunatha Gudekote ,&nbsp;Prathiksha ,&nbsp;Rajashekhar Choudhari ,&nbsp;Hanumesh Vaidya ,&nbsp;Kerehalli Vinayaka Prasad","doi":"10.1016/j.padiff.2026.101368","DOIUrl":"10.1016/j.padiff.2026.101368","url":null,"abstract":"<div><div>The present study theoretically investigates the mixed convection flow and heat transfer of a Ree-Eyring non-Newtonian fluid in a vertical channel driven by rhythmic membrane contraction. The main objective of this work is to understand how variable fluid properties, thermal effects, and non-Newtonian behaviour influence fluid motion, pumping performance, and heat transfer in membrane-based microfluidic systems. The pressure gradient induced by a moving membrane, combined with buoyancy forces, drives the fluid through a vertical microchannel. To capture realistic thermal behaviour, temperature-dependent viscosity and thermal conductivity are incorporated into the model. Variable viscosity and variable thermal conductivity are considered to accommodate variable fluid properties. The basic nonlinear equations are then derived using the assumptions of a small Reynolds number, a long wavelength, and the lubrication approximation. Because of the nonlinearity of the governing equations, a regular perturbation technique is developed to obtain semi-analytical expressions for the velocity and temperature distributions. From these obtained velocity and temperature fields, the pressure gradient, skin friction, Nusselt number, flow rate, and stream function were then evaluated. Extensive parametric analysis has been performed in MATLAB R2024b to investigate the influence of variable viscosity, variable thermal conductivity, the heat-source parameter, the Grashof number, and the Ree-Eyring fluid parameter on the flow and thermal characteristics. Results indicate that variable viscosity improves flow behaviour, whereas heat generation and buoyancy forces significantly affect pumping and heat characteristics. The present findings provide useful guidance for the design and optimisation of thermally controlled micro-pumps, MEMS cooling devices, lab-on-chip technologies, and biomedical microchannels that require accurate regulation of fluid flow and heat transfer.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"18 ","pages":"Article 101368"},"PeriodicalIF":0.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148230622","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":"Significance of thermal jump in hybrid nanomaterial with nonlinear thermal radiation and porous space","authors":"M. Ibtesam ,&nbsp;S. Mengjie ,&nbsp;B. Ahmed","doi":"10.1016/j.padiff.2026.101346","DOIUrl":"10.1016/j.padiff.2026.101346","url":null,"abstract":"<div><div>Investigators have commonly recognized hybrid nanomaterials for their involvement in automobiles, solar heaters, battery-powered engines, pharmaceutical phenomena, domestic refrigerator, food processing, heating, cooling in manufacturing, ventilation and air conditioning. Especially the magnetohydrodynamic (MHD) hybrid nanomaterials are significant for Magnetic Resonance Imaging (MRI), blood oxygenation, respiratory process, X-ray imaging, medicinal delivery, gene transport, DNA probing process, cell biology, infectious diseases, photoacoustic imaging, nervous disorders and treatment of cancer, dropsy, jaundice and hernias. Hence the current research is organized for peristalsis involving hybrid nanofluid with electroosmotic effect. Iron oxide (<em>Fe</em>₃<em>O</em>₄) and gold (Au) are taken as the nanoparticles. Unlike the classical concept, the nonlinear version of thermal radiation is examined. Corrugated symmetric flow configuration is adopted. Impact of magnetohydrodynamics through Lorentz force is retained. Porous space is characterized by invoking Darcy-Forchheimer relation. Mixed convection is not ignored. Analysis is carried out for velocity and thermal slip aspects. Feature of electroomosis is described by Nernst-Planck and Poisson expressions. Dissipation, Joule heating and heat generation in thermal equation are present. The analysis is executed with consideration of large wavelengths and low Reynolds numbers. Resulting problems after invoking lubrication approach are solved numerically. Thermal field, velocity and pressure gradient are graphically analyzed through outcome of influential parameters. Heat transfer rate is probed. Here the Darcy and Forchheimer parameters for velocity have opposite response. Temperature by thermal jump parameter is enhanced. As expected the nanomaterials have more heat transfer rate when compared with hybrid nanofluids.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101346"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147397040","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":"Comment on the paper \"MD. Shamshuddin, Balasani Srinitha, S.O. Salawu, M. Sundeer Ram, Partial Differential Equations in Applied Mathematics 13 (2025) 101,100\"","authors":"Asterios Pantokratoras","doi":"10.1016/j.padiff.2026.101341","DOIUrl":"10.1016/j.padiff.2026.101341","url":null,"abstract":"<div><div>A serious error exists in the above paper.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101341"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146189146","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":"Bell wavelets method to solve class of fractional differential equations arising in fluid mechanics","authors":"Pooja Yadav ,&nbsp;Shah Jahan ,&nbsp;Kottakkaran Sooppy Nisar","doi":"10.1016/j.padiff.2025.101336","DOIUrl":"10.1016/j.padiff.2025.101336","url":null,"abstract":"<div><div>This study introduces a new Bell wavelet matrix method to solve a class of fractional differential equations arising in fluid mechanics. The class under consideration comprises the fractional relaxation-oscillation equation (R-OE) as a special case. In this work, the Bell wavelets are constructed using the Bell polynomials and their properties. The fractional operational matrix of integration is developed using block pulse functions (BPFs). The primary benefit of the suggested approach lies in its ability to convert these fractional R-OE into a set of algebraic equations, making them well-suited for computer programming. The present approach’s effectiveness and performance are shown by four test problems. By comparing the solutions obtained through this method with exact solutions and existing methods, we gain insight into the accuracy and reliability of the approach.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101336"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038120","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":"Quintic nonlinearity enables modulation instability in normal dispersion regimes for spectral control","authors":"Sujata Vedi ,&nbsp;Mohit Sharma ,&nbsp;Monika Goyal ,&nbsp;Yogesh Sharma","doi":"10.1016/j.padiff.2026.101339","DOIUrl":"10.1016/j.padiff.2026.101339","url":null,"abstract":"<div><div>Modulation instability in cubic-quintic nonlinear media is rigorously analyzed using an extended nonlinear Schrödinger equation framework. Results demonstrate that focusing quintic nonlinearity (<em>γ</em>₅ &gt; 0) reduces the critical power for instability onset by 40%–60% relative to cubic systems while defocusing terms (<em>γ</em>₅ &lt; 0) elevate thresholds by 60%–80%. The instability bandwidth achieving 80% spectral broadening with <em>γ</em>₅ &gt; 0. Septic nonlinearity (<em>γ</em>₇ &gt; 0) amplifies maximum gain by 30%–50% at high intensities. Crucially, <em>γ</em>₅ &gt; 0 enables MI in normal dispersion regimes (<em>β</em>₂ &gt; 0) unattainable in purely cubic media. These findings advance predictive models for semiconductor-doped photonic crystal fibers and colloidal quantum dots. Applications include optimized supercontinuum sources, tunable optical frequency combs, and terahertz pulse generation systems with enhanced spectral control.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101339"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146189144","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":"Retraction Notice to “Analysis of boundary layer flow of a Jeffrey fluid over a stretching or shrinking sheet immersed in a porous medium” [Partial Differential Equations in Applied Mathematics 12 (2024) 100951]","authors":"Nagaraju B ,&nbsp;N Kishan ,&nbsp;Jagadish V. Tawade ,&nbsp;Pandikani Meenapandi ,&nbsp;Barno Abdullaeva ,&nbsp;M. Waqas ,&nbsp;Manish Gupta ,&nbsp;Nadia Batool ,&nbsp;Furqan Ahmad","doi":"10.1016/j.padiff.2026.101348","DOIUrl":"10.1016/j.padiff.2026.101348","url":null,"abstract":"","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101348"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147396518","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 non-linear motion on mixed convection in viscous fluids with temperature-dependent thermal conductivity and oscillating thermal wave","authors":"M.M. Nour ,&nbsp;Abdur Rehman ,&nbsp;Abdallah aldurayhim ,&nbsp;Muhammad Ashraf ,&nbsp;A.M. Rashad ,&nbsp;Hossam A. Nabwey","doi":"10.1016/j.padiff.2025.101333","DOIUrl":"10.1016/j.padiff.2025.101333","url":null,"abstract":"<div><div>This study investigates the effects of non-linear motion on mixed convection viscous fluid flow, incorporating thermal conductivity inversely proportional to a linear function of temperature under the influence of oscillating thermal waves. To provide a comprehensive understanding, the research explores convective heat transfer in the presence of vorticity. The governing equations, including continuity, momentum, and heat equations, are formulated to represent the intricate non-linear dynamics of fluid flow and heat transfer. These equations are rendered dimensionless using appropriate scaling variables and subsequently transformed into steady and unsteady forms to address varying thermal and flow conditions. A Gaussian elimination approach, combined with a primitive variable formulation, is employed for numerical computation, alongside the finite difference method. Computational solutions are developed using FORTRAN Laher-90, with graphical and tabular results presented via Tecplot-360 to analyze transient shear stress (τ_<em>s</em>​) and transient heat transfer (τ_<em>t</em>) influenced by oscillating thermal waves. The findings reveal critical insights into the interplay between vorticity, non-linear fluid behavior, and thermal oscillations, contributing to advancements in optimizing convective heat transfer mechanisms. The findings show that in steady-state conditions, temperature distribution and flow velocity increase with higher values of the thermal conductivity variation parameter (ς). In the unsteady state, transient shear stress τₛ exhibits higher wave amplitude at ς = 0.2, followed by slight changes in phase angle at different values. However, transient heat transfer τ_t decreases in wave magnitude as ς increases.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"17 ","pages":"Article 101333"},"PeriodicalIF":0.0,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145791934","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}