Partial Differential Equations in Applied Mathematics最新文献

{"title":"Fourier series approximation of fractal functions","authors":"C. Kavitha ,&nbsp;A. Gowrisankar ,&nbsp;Fathalla A. Rihan ,&nbsp;R. Rakkiyappan","doi":"10.1016/j.padiff.2024.101038","DOIUrl":"10.1016/j.padiff.2024.101038","url":null,"abstract":"<div><div>The fractal function is generated as an attractor of iterated function systems. This article examines the Fourier series representation of fractal interpolation functions, including affine and non-affine functions with different vertical scaling factors, as a way of expressing fractal functions explicitly. The given concepts have been illustrated with appropriate examples and graphical approaches.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101038"},"PeriodicalIF":0.0,"publicationDate":"2024-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Abundant closed-form solitary solutions of a nonlinear neurobiological model for analyzing numerous signal transmission behaviors through the neuron using recent scheme","authors":"M. Nurul Islam ,&nbsp;M. Al-Amin ,&nbsp;M. Ali Akbar","doi":"10.1016/j.padiff.2024.101051","DOIUrl":"10.1016/j.padiff.2024.101051","url":null,"abstract":"<div><div>This study is to construct the solitary wave solutions to the nonlinear Fitzhugh-Nagumo (FN) model. The Fitzhugh-Nagumo(FN) model is a simplification form of the Hodgkin-Huxley model for nerve's impulse transmission through the nerve fibers, it also described the noise formations in circuit theory, the intercellular trigger waves and more. This is indubitably very important mathematical model in various neurobiological sciences and engineering applications. The generalized exponential rational function (GERF) technique is imposed to the considered model which accumulates different wave solutions in suitable form. In addition, we analyze the effects of wave velocity on the attained solutions, to realize the dynamical behavior of the related phenomenon. The attained results confirm the efficiency and consistency of the considered technique.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101051"},"PeriodicalIF":0.0,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143164863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Heat transfer with magnetic force and slip velocity on non-Newtonian fluid flow through a porous medium","authors":"Muhammad Ramzan ,&nbsp;Muhammad Shahryar ,&nbsp;Shajar Abbas ,&nbsp;Muhammad Amir ,&nbsp;Shaxnoza Ravshanbekovna Saydaxmetova ,&nbsp;Rashid Jan ,&nbsp;Afnan Al Agha ,&nbsp;Hakim AL Garalleh","doi":"10.1016/j.padiff.2024.101033","DOIUrl":"10.1016/j.padiff.2024.101033","url":null,"abstract":"<div><div>This study investigates the combined effects of heat and mass transfer on free convection flow of Brinkman fluid over a plate embedded in porous media, focusing on applications in engineering and environmental science where efficient thermal and mass transport are essential. This research addresses the complexity of controlling fluid behavior in porous structures, where factors like heat, mass, and momentum fluxes play a critical role. The Atangana–Baleanu fractional derivative is employed to model the flow, integrating Fourier’s and Fick’s laws to handle heat and mass transfer, with added effects from slip conditions and chemical reactions to capture a more realistic flow scenario. The governing partial differential equations are transformed into dimensionless form and solved semi-analytically using the Laplace transform method. Model validation is achieved by comparing results obtained through algorithmic solutions, confirming the robustness of the fractional approach by taking the values of fractional parameter <span><math><mi>γ</mi></math></span> in the range <span><math><mrow><mn>0</mn><mo>.</mo><mn>2</mn><mo>≤</mo><mi>γ</mi><mo>≤</mo><mn>1</mn></mrow></math></span>, whereas the values of slip parameter <span><math><mi>λ</mi></math></span> lies in the range <span><math><mrow><mn>0</mn><mo>≤</mo><mi>λ</mi><mo>≤</mo><mn>0</mn><mo>.</mo><mn>8</mn></mrow></math></span>. The model also discussed the effect of magnetic lines of force relative to fluid as well as relative to plate by taking values of <span><math><mi>ϵ</mi></math></span> is equal to 0 and 1. Key findings reveal that increasing thermal and mass Grashof numbers by 10% results in a 12% rise in fluid velocity, emphasizing the positive impact of buoyancy forces on flow acceleration. Conversely, stronger magnetic fields, chemical reactions, and the Brinkman parameter exhibit a damping effect, reducing velocity by up to 8% when these parameters increase. Additionally, heat sink intensification further slows down fluid motion. A comparative analysis between fractionalized and classical models highlights that fractional techniques capture flow behaviors more precisely, revealing a more flexible and accurate description of convection phenomena. This model advances previous studies by demonstrating that fractional derivatives significantly enhance the prediction of fluid behavior in porous media, underscoring the effectiveness of fractional modeling for complex convection processes. These insights position the fractional approach as a preferred alternative to classical methods for simulating real-world convection flows, offering greater applicability to porous media transport phenomena in engineering and environmental systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101033"},"PeriodicalIF":0.0,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the reduction and solution of the reverse space-time nonlocal Fokas–Lenells equation","authors":"Sohaib Al-Ramadhani","doi":"10.1016/j.padiff.2024.101046","DOIUrl":"10.1016/j.padiff.2024.101046","url":null,"abstract":"<div><div>Fokas–Lenells equation is a dynamical system used to model propagation of nonlinear pulses. Different reductions of the Fokas–Lenells system lead to various formulas of the equation including local and nonlocal versions. In addition, different approaches have been employed in the literature to explore the solutions of the Fokas–Lenells equations. In this paper we propose a reverse space-time reduction that leads to a nonlocal version of the Fokas–Lenells model. Furthermore, we present a calculation of the solution of the proposed equation based on known results in the literature from the Hirota bilinear direct method. The one-soliton and two-soliton solutions have been explicitly described and graphically illustrated.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101046"},"PeriodicalIF":0.0,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On some explicit solitary wave patterns for a generalized nonlinear reaction–diffusion equation with conformable temporal fractional derivative","authors":"Muhammad Jawaz ,&nbsp;Jorge E. Macías-Díaz ,&nbsp;Syed A. Aqeel ,&nbsp;Nauman Ahmed ,&nbsp;Muhammad Z. Baber ,&nbsp;María G. Medina-Guevara","doi":"10.1016/j.padiff.2024.101036","DOIUrl":"10.1016/j.padiff.2024.101036","url":null,"abstract":"<div><div>Soliton solutions of a <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional reaction–diffusion problem are derived in the present work using the generalized Riccati equation mapping method. The model captures the time evaluation of disturbance and addresses modeling real-world phenomena such as turbulence, traffic flow, heat and fluid transport, and gas dynamics. To start with, the nonlinear conformable time fractional transformation is employed to derive a general nonlinear ordinary differential equation from the nonlinear reaction–diffusion equation. Next, we find exact solutions of this model through the application of the generalized Riccati equation mapping approach. This methodology yields numerous families of solutions, including solitary waves and solitons. We obtain various forms of solutions, including singular, dark, kink, and bright solitons. For illustration purposes, we provide graphs of some exact solutions in the form of three-dimensional plots, two-dimensional plots and contour graphs.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101036"},"PeriodicalIF":0.0,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Variational equation for discontinuous delayed systems","authors":"D.D. Bain","doi":"10.1016/j.padiff.2024.101034","DOIUrl":"10.1016/j.padiff.2024.101034","url":null,"abstract":"<div><div>For discontinuous delay differential equations, we derive and analyze the variational equation (also known as the linearization), which describes the evolution of infinitesimal perturbations to initial conditions. This variational equation incorporates delta functions that account for jumps in the right-hand side of the original equation. We establish fundamental properties of the solutions of this equation and explore its applications, which include the generalization of the theory and computational methods of Lyapunov exponents for discontinuous delayed systems, providing a powerful tool for studying stability and chaos in such systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101034"},"PeriodicalIF":0.0,"publicationDate":"2024-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Thermo-diffusion, diffusion-thermo impacts on heat and mass transfer casson fluid flow with porous medium in the presence of heat generation and radiation","authors":"Vasa Vijaya Kumar ,&nbsp;MN. Raja Shekar ,&nbsp;Shankar Goud Bejawada","doi":"10.1016/j.padiff.2024.101039","DOIUrl":"10.1016/j.padiff.2024.101039","url":null,"abstract":"<div><div>In this study, we explore the impact that heat absorption or generation plays in time-dependent free MHD convective transport across a vertical porous plate that is subjected to thermal radiation. With the help of similarity transformation, the governing equations are converted, and the dimensionless equations that are produced as a consequence are solved numerically with the help of the finite difference approach(FDM). Figures and tables are used to illustrate and analyse in depth the impact that a variety of controlling factors have on the flow fields throughout the flow process. The numerical findings that we obtained are more in line with the study that was published. The findings show that the influence of the Casson parameter rises velocity. The velocity and concentration of the nanofluid are improved by raising the values of the Soret number factor. The velocity and temperature distributions improve as the Dufour number rises.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101039"},"PeriodicalIF":0.0,"publicationDate":"2024-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A discrete extension of the Lindley distribution for health and sustainability data: Theoretical insights and decision-making applications","authors":"Mahmoud El-Morshedy ,&nbsp;Mohamed S. Eliwa ,&nbsp;Abhishek Tyagi ,&nbsp;Hend S. Shahen","doi":"10.1016/j.padiff.2024.101013","DOIUrl":"10.1016/j.padiff.2024.101013","url":null,"abstract":"<div><div>Integrating SDG 3 (Good Health and Well-Being) with an innovative discrete probability model for lifetime data provides a comprehensive approach to achieving sustainable health outcomes and analyzing lifetime data within sustainability frameworks. This model captures the discrete nature of lifetime measurements frequently found in patient records, equipment longevity, and treatment interval by drawing on the Kumaraswamy family for accuracy. Its essential statistical features, including hazard rate, moments, dispersion index, skewness, and entropy, support robust health data analysis, enhancing SDG 3 by improving our understanding of survival trends in patients and medical devices. Additionally, the model’s adaptability to asymmetric dispersion across various kurtosis types (mesokurtic, platykurtic, and leptokurtic) allows it to address variability in health outcomes influenced by demographic or treatment factors. The flexible hazard rate function spanning decreasing, bathtub-shaped, and constant rates makes it well-suited for a range of health applications, from chronic disease management to mortality studies. Furthermore, its capacity to handle zero-inflated and over- or under-dispersed data, commonly seen in health research, enables a more refined public health analysis crucial for SDG 3. With maximum likelihood estimation for parameter fitting, the model has been validated in practical sustainability contexts, such as monitoring patient follow-ups, evaluating device reliability, and examining disease progression, offering valuable insights for sustainable health interventions and effective resource use.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101013"},"PeriodicalIF":0.0,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143165055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Carreau fluid flow analysis with inclined magnetic field and melting heat transfer","authors":"Rasheed Khan ,&nbsp;Salman Zeb ,&nbsp;Zakir Ullah ,&nbsp;Muhammad Yousaf ,&nbsp;Inna Samuilik","doi":"10.1016/j.padiff.2024.101030","DOIUrl":"10.1016/j.padiff.2024.101030","url":null,"abstract":"<div><div>In this study, we consider melting heat transfer and inclined magnetic field impacts on the flow of Carreau fluid past a stretched permeable sheet in a along with influences of variable thermal conductivity, diffusion-thermo, and thermal-diffusion. The problem is formulated as a system of nonlinear partial differential equations and using similarity transformations these are converted to non-linear ordinary differential equations. Numerical solutions of the problem are investigated via numerical algorithm by employing Runge–Kutta–Fehlberg fourth–fifth order scheme along with shooting method and the results are reported graphically for velocity, temperature, and concentration profiles. The velocity profile enhanced against the growing power law index, Weissenberg number, and melting parameter while it declines for magnetic parameter, angle of inclination, and porosity parameter. The temperature profile increases with modified Dufour parameter and Soret number while it diminishes for magnetic, thermal conductivity, and melting parameters. The concentration profile enhances for magnetic parameter while diminishes for modified Dufour parameter, Schmidt and Soret numbers. The numerical data is obtained for physical quantities of engineering interests against the various parameters. The skin friction results against the magnetic parameter are compared with previous published studies in the literature which validated the accuracy of our numerical findings.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101030"},"PeriodicalIF":0.0,"publicationDate":"2024-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluating formation of interfacial nanolayer of Au/Cu with graphene nanoparticles along with magnetic-morphologies by considering CattaneoChristov heat flux dynamics","authors":"S. Bilal ,&nbsp;M.Z.A. Qureshi ,&nbsp;M. Awais ,&nbsp;Muhammad Farooq","doi":"10.1016/j.padiff.2024.101020","DOIUrl":"10.1016/j.padiff.2024.101020","url":null,"abstract":"<div><div>Multilayer graphene (MLG) is essential for the development of advanced electronic devices because of its exceptional electrical, mechanical, and chemical properties. Thus, integrating an interfacial nanolayer metallic layer is crucial for optimizing MLG's thermal properties of MLGs and their use in advanced practical applications. Some mesmerizing applications of MLG include memory devices, LED's, composite material coatings, wearable sensors, photonics, fuel cells, and water desalination. Simultaneously, the exploration of ternary nanofluids (TNF) offers transformative potential for heat transfer and fluid dynamics. By combining with metallic oxide nanoparticles, TNFs create new synergies and functionalities that enhance their performance. This research introduces advanced models, such as the CattaneoChristov heat flux (CCHF) model and magneto-hydrodynamic (MHD) effects, to reveal TNFs’ latent capabilities of the TNFs. Detailed numerical analysis based on the partial differential equation system of nanolayer morphology and fluid behavior provides novel insights into optimizing heat exchange and fluid flow in porous discs. Furthermore, our study examined the complex interactions between magnetic fields, temperature gradients, and concentration profiles, offering critical insights for cutting-edge engineering applications. It is deduced from the results that the effective thermal conductivity increases up to 17.06 % in comparison to the non-effective thermal conductivity with changes in the ternary nanoparticle volume fraction from 2 % to 7 %. In addition, it is inferred that thermal flux at the surface of the lower disk increases to 4.9 % and 5.9 % with respect to the variation in the nanolayer thickness and radius of the ternary nanoparticles, respectively. The skin friction coefficient exhibits a significant increase up to 75 % in response to variation in magnetic field strength, ranging from 0.1 to 1.3. A substantial reduction in boundary-layer thickness up to 52 % is observed when the volume fraction exceeds 3 %.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101020"},"PeriodicalIF":0.0,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163394","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}