Partial Differential Equations in Applied Mathematics最新文献

{"title":"Exploring the dynamics of leprosy transmission with treatment through a fractal–fractional differential model","authors":"Khadija Tul Kubra ,&nbsp;Rooh Ali ,&nbsp;Bushra Ujala ,&nbsp;Samra Gulshan ,&nbsp;Tayyaba Rasool ,&nbsp;Mohamed Reda Ali","doi":"10.1016/j.padiff.2024.100909","DOIUrl":"10.1016/j.padiff.2024.100909","url":null,"abstract":"<div><div>Leprosy continues to be a significant public health challenge in many parts of the world, necessitating novel approaches to understanding and controlling its transmission. The dynamics of leprosy are examined in this study by means of a caputo fabrizio fractal–fractional differential system model. Leprosy transmission and treatment are complex and non-linear processes that can be captured by fractal–fractional derivatives. The temporal progression of the disease is the primary focus of our mathematical analysis, which evaluates a variety of parameter values, including initial population densities and compartmental transitions. Through simulations, we examine the impact of critical parameters on the severity and spread of diseases, as well as the rates of recovery and treatment. Numerical results of the model offer valuable insights into the impact of these parameters on leprosy dynamics, which is beneficial for public health interventions. The stability analysis of the model identifies supplementary conditions that are necessary for the success of disease control. By incorporating these novel mathematical techniques, we hope to improve our understanding of leprosy transmission and ultimately contribute to more effective control strategies. Based on our findings, additional studies investigating the relation between population density, treatment accessibility, and recovery rates are warranted. We hope that by graphically representing the relationships between these factors, we can draw attention to the possibility of targeted interventions that can reduce the transmission of leprosy. This study provides a strong basis for future studies on infectious disease modeling and aids leprosy-affected communities in developing strategies to mitigate the disease’s impact.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100909"},"PeriodicalIF":0.0,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529094","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":"Entwining tetrahedron maps","authors":"Pavlos Kassotakis","doi":"10.1016/j.padiff.2024.100949","DOIUrl":"10.1016/j.padiff.2024.100949","url":null,"abstract":"<div><div>We present three non-equivalent procedures to obtain <em>entwining (non-constant) tetrahedron maps</em>. Given a tetrahedron map, the first procedure incorporates its underlying symmetry group. With the second procedure we obtain several classes of entwining tetrahedron maps by considering certain compositions of <em>pentagon</em> with <em>reverse-pentagon maps</em> which satisfy certain compatibility relations the so-called <em>ten-term relations</em>. Using the third procedure, provided that a given tetrahedron map admits at least one <em>companion map (partial inverse)</em>, we obtain entwining set theoretical solutions of the tetrahedron equation.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100949"},"PeriodicalIF":0.0,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529120","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":"Tensor product solutions of certain Abstract Cauchy problems of Euler type","authors":"Sharifa Al-Sharif ,&nbsp;Batool Momani ,&nbsp;Jamila Jawdat","doi":"10.1016/j.padiff.2024.100957","DOIUrl":"10.1016/j.padiff.2024.100957","url":null,"abstract":"<div><div>Our concern in this paper, is to find exact solutions, using tensor product techniques, of two types of second order homogeneous Abstract Cauchy problems of the following forms <span><span><span><math><mrow><msup><mrow><mi>u</mi></mrow><mrow><mo>″</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>C</mi><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>F</mi><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>,</mo></mrow></math></span></span></span> and <span><span><span><math><mrow><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mn>2</mn><mi>t</mi><mi>C</mi><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>+</mo><mi>F</mi><mi>u</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mo>.</mo></mrow></math></span></span></span> The initial conditions to be used are <span><span><span><math><mrow><mi>u</mi><mrow><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow><mo>=</mo><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mspace></mspace><msup><mrow><mi>u</mi></mrow><mrow><mo>′</mo></mrow></msup><mrow><mo>(</mo><msub><mrow><mi>t</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>)</mo></mrow><mo>=</mo><msubsup><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>,</mo></mrow></math></span></span></span> where <span><math><mi>C</mi></math></span> and <span><math><mi>F</mi></math></span> are closed linear operators that are densely defined on a Banach space <span><math><mi>Y</mi></math></span>, <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>,</mo><mspace></mspace><msubsup><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>′</mo></mrow></msubsup><mo>∈</mo><mi>Y</mi></mrow></math></span> and <span><math><mrow><mi>u</mi><mo>∈</mo><msup><mrow><mi>C</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>I</mi><mo>,</mo><mi>Y</mi><mo>)</mo></mrow><mo>.</mo></mrow></math></span></div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100957"},"PeriodicalIF":0.0,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528092","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":"Investigation of lump, breather and multi solitonic wave solutions to fractional nonlinear dynamical model with stability analysis","authors":"M.A. El-Shorbagy ,&nbsp;Sonia Akram ,&nbsp;Mati ur Rahman","doi":"10.1016/j.padiff.2024.100955","DOIUrl":"10.1016/j.padiff.2024.100955","url":null,"abstract":"<div><div>In the current research, the new extended direct algebraic method (NEDAM) and the symbolic computational method, along with different test functions, the Hirota bilinear method, are capitalized to secure soliton and lump solutions to the <span><math><mrow><mo>(</mo><mn>2</mn><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-dimensional fractional telecommunication system. Consequently, we derive soliton solutions with sophisticated structures, such as mixed trigonometric, rational, hyperbolic, unique, periodic, dark-bright, bright-dark, and hyperbolic. We also developed a lump-type solution that includes rogue waves and breathers for curiosity’s intellect. These features are important for controlling extreme occurrences in optical communications. Additionally, we investigate modulation instability (MI) in the context of nonlinear optical fibres. Understanding MI is essential for developing systems that may either capitalize on its positive features or mitigate its adverse effects. Also, a comprehensive sensitivity analysis of the observed model is carried out to evaluate the influence of different factors. 3D surfaces and 2D visuals, contours, and density plots of the outcomes are represented with the help of a computer application. Our findings demonstrate the potential of using soliton theory and advanced nonlinear analysis methods to enhance the performance of telecommunication systems.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100955"},"PeriodicalIF":0.0,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142445214","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":"An iterative approach for addressing monotone inclusion and fixed point problems with generalized demimetric mappings","authors":"Anjali ,&nbsp;Seema Mehra ,&nbsp;Renu Chugh ,&nbsp;Dania Santina ,&nbsp;Nabil Mlaiki","doi":"10.1016/j.padiff.2024.100953","DOIUrl":"10.1016/j.padiff.2024.100953","url":null,"abstract":"<div><div>Throughout this study, we present a new algorithm for finding the common solution of a finite family of monotone inclusion and the fixed point problem of a finite family of generalized demimetric operators in the context of a real Hilbert space and show its strong convergence. Moreover, we utilize our result to solve the minimization problem.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100953"},"PeriodicalIF":0.0,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142437666","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":"Three-dimensional stagnation point motion of bioconvection nanofluid via moving stretching sheet with convective and anisotropic slip condition","authors":"Nune Pratyusha ,&nbsp;Nainaru Tarakaramu ,&nbsp;Suresh Babu R ,&nbsp;V.K. Somasekhar Srinivas ,&nbsp;Furqan Ahmad ,&nbsp;M. Waqas ,&nbsp;Barno Abdullaeva ,&nbsp;Manish Gupta","doi":"10.1016/j.padiff.2024.100958","DOIUrl":"10.1016/j.padiff.2024.100958","url":null,"abstract":"<div><div>The current article deals with the SM of a NFs on a 3D moving surface containing bioconvection, microorganisms, and convective conditions over anisotropic slip. This work reports describes the characteristics of bioconvection aspects of nanofluid containing microorganisms with anisotropic slip condition. The study may be important from the application point of view in microfluidic devices, antibiotics, enhanced oil recovery and many other areas. Applying the similarity variables, the basic gov. Eqs are translated to ordinary ones, and such Eqs are calculate by R-K-F fourth order programming with shooting scheme by MATLAB software. The physical parameters on the moving surface are explained in detail via graphs. We found that the temperature increases with a higher revolution and larger numerical numbers (convection parameter), while the HTR declined for various values of the SFP. The HTR enhances with surface convection, and therefore, the convection condition is helpful in reducing the viscous drag on the moving SS.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100958"},"PeriodicalIF":0.0,"publicationDate":"2024-10-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142528095","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":"New modifications of natural transform iterative method and q-homotopy analysis method applied to fractional order KDV-Burger and Sawada–Kotera equations","authors":"Muayyad Mahmood Khalil ,&nbsp;Siddiq Ur Rehman ,&nbsp;Ali Hasan Ali ,&nbsp;Rashid Nawaz ,&nbsp;Belal Batiha","doi":"10.1016/j.padiff.2024.100950","DOIUrl":"10.1016/j.padiff.2024.100950","url":null,"abstract":"<div><div>This manuscript presents enhanced versions of two methods: the natural transform iterative method (NTIM) and the q-homotopy analysis method (q-HAM). These methods harness concepts from Fractional Calculus, particularly leveraging the Caputo fractional derivative operator, to successfully manage the complexities of fractional-order systems. To validate their accuracy and efficiency, we applied the proposed techniques to FPDEs like the fractional-order KDV-Burger and fifth-order Sawada–Kotera equations. Our outcomes, which closely resemble the exact solutions, demonstrate how useful NTIM and q-HAM are for solving difficult FPDEs and improving the study of fractional calculus.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100950"},"PeriodicalIF":0.0,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142442531","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":"Anisotropic error estimator for the Stokes–Biot system","authors":"Houédanou Koffi Wilfrid","doi":"10.1016/j.padiff.2024.100952","DOIUrl":"10.1016/j.padiff.2024.100952","url":null,"abstract":"<div><div>This paper presents an a posteriori error analysis for the problem defining the interaction between a free fluid and poroelastic structure approximated by finite element methods on anisotropic meshes in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span>, <span><math><mrow><mi>d</mi><mo>=</mo><mn>2</mn></mrow></math></span> or 3. <em>Korn’s inequality</em> for piecewise linear vector fields on anisotropic meshes is established and is applied to nonconforming finite element method. Then the existence and uniqueness of the approximation solution are deduced for conforming and nonconforming cases. With the obtained finite element solutions, local error indicators and a global estimator are generated, demonstrating reliability and efficiency. <em>The efficiency</em> is proved by means of bubble functions and the corresponding anisotropic inverse inequalities. In order to prove the <em>reliability</em>, it is vital that an anisotropic mesh corresponds to the anisotropic function under consideration. To measure this correspondence, a so-called <em>matching function</em> is defined, and its discussion shows it to be useful tool. With its help, the <em>upper error bound</em> is shown by means of the corresponding anisotropic interpolation estimates and <em>a special Helmholtz decomposition</em> in both media.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100952"},"PeriodicalIF":0.0,"publicationDate":"2024-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529122","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 study on the fractional-order COVID-19 SEIQR model and parameter analysis using homotopy perturbation method","authors":"Mominul Islam,&nbsp;M. Ali Akbar","doi":"10.1016/j.padiff.2024.100960","DOIUrl":"10.1016/j.padiff.2024.100960","url":null,"abstract":"<div><div>In this article, we present a fractional-order susceptible-exposed-infected-quarantine-recovered (SEIQR) model to analyze the dynamics of the COVID-19 pandemic. The model includes susceptible (<em>S</em>), exposed (<em>E</em>), infected (<em>I</em>), quarantined (<em>Q</em>), and recovered (<em>R</em>) populations and uses a fractional-order differential equation to provide a further accurate representation of the disease's progression. We employ the homotopy perturbation method (HPM) to derive analytical solutions and the Runge-Kutta fourth-order (RK4) method to obtain numerical solutions. The results indicate that the fractional-order model, particularly for a fractional parameter α = 0.40, provides better accuracy and stability compared to the classical integer-order model. This study highlights the importance of fractional-order modeling in understanding the spread of COVID-19 and suggests its potential application in predicting and controlling future epidemics.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100960"},"PeriodicalIF":0.0,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529121","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":"Innovative approache for the nonlinear atangana conformable Klein-Gordon equation unveiling traveling wave patterns","authors":"Hadi Rezazadeh ,&nbsp;Mohammad Ali Hosseinzadeh ,&nbsp;Lahib Ibrahim Zaidan ,&nbsp;Fatima SD. Awad ,&nbsp;Fiza Batool ,&nbsp;Soheil Salahshour","doi":"10.1016/j.padiff.2024.100935","DOIUrl":"10.1016/j.padiff.2024.100935","url":null,"abstract":"<div><div>The aim of current work is to establish novel traveling wave solutions of the nonlinear Atangana conformable Klein - Gordon equation using a new extended direct algebraic technique. The Klein - Gordon equation is the relativistic state of the Schrödinger equation with a second - order time derivative and zero spin. Complex wave variable transformation is used to convert Atangana conformable nonlinear differential equation into an ordinary differential equation. Using the proposed technique based on Maple software structure, various types of solutions, such as, generalized trigonometric, generalized hyperbolic, and exponential functions, are established. When special parameteric values are considered for this method, solitary wave solutions can be obtained through other methods, such as the (<span><math><mfrac><msup><mi>G</mi><mo>′</mo></msup><mi>G</mi></mfrac></math></span>)-expansion method, the modified Kudryashov method, the sub-equation method, and so forth. A physical explanation is provided for the solutions under consideration to enhance comprehension of the physical phenomena resulting from the obtained solutions, provided that the physical parameters are set appropriately using 3D, 2D, and contour simulations. The results demonstrated that the new extended direct algebraic method provides a more potent mathematical tool for solving numerous more nonlinear partial differential equations with the aid of symbolic computation.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100935"},"PeriodicalIF":0.0,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142529092","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}