International Journal of Differential Equations最新文献

{"title":"A Fractional-Order Eco-Epidemiological Leslie–Gower Model with Double Allee Effect and Disease in Predator","authors":"Emli Rahmi, I. Darti, A. Suryanto, T. Trisilowati","doi":"10.1155/2023/5030729","DOIUrl":"https://doi.org/10.1155/2023/5030729","url":null,"abstract":"In this paper, a fractional order of a modified Leslie–Gower predator-prey model with disease and the double Allee effect in predator population is proposed. Then, we analyze the important mathematical features of the proposed model such as the existence and uniqueness as well as the non-negativity and boundedness of solutions to the fractional-order system. Moreover, the local and global asymptotic stability conditions of all possible equilibrium points are investigated using Matignon’s condition and by constructing a suitable Lyapunov function, respectively. Finally, numerical simulations are presented to verify the theoretical results. We show numerically the occurrence of two limit cycles simultaneously driven by the order of the derivative, the bistability phenomenon for both the weak and strong Allee effect cases, and more dynamic behaviors such as the forward, backward, and saddle-node bifurcations which are driven by the transmission rate. We have found that the risk of extinction for the predator with a strong Allee effect is much higher when the spread of disease is relatively high.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41592550","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":"Existence and Uniqueness Solution of the Model of Enzyme Kinetics in the Sense of Caputo–Fabrizio Fractional Derivative","authors":"G. K. Edessa","doi":"10.1155/2022/1345919","DOIUrl":"https://doi.org/10.1155/2022/1345919","url":null,"abstract":"In this paper, a model of the rates of enzyme-catalyzed chemical reactions in the sense of Caputo–Fabrizio a fractional derivative was investigated. Its existence and uniqueness as a solution of the model was proved by setting different criteria. An iterative numerical scheme was provided to support the findings. In order to verify the applicability of the result, numerical simulations using the MATLAB software package that confirms the analytical result was lucidly shown.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42012248","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":"Solutions of Three Dimensional Nonlinear Klein-Gordon Equations by Using Quadruple Laplace Transform","authors":"W. Ibrahim, Mesele Tamiru","doi":"10.1155/2022/2544576","DOIUrl":"https://doi.org/10.1155/2022/2544576","url":null,"abstract":"This study focuses on solving three-dimensional non-linear Klein-Gordon equations of four variables by using the quadruple Laplace transform method coupled with the iterative method. This study was designed in order to show the quadruple Laplace transform with an iterative method for solving three-dimensional nonlinear Klein-Gordon equations. The quadruple Laplace transform with the iterative method was aimed at getting analytical solutions of three-dimensional nonlinear Klein-Gordon equations. Exact solutions obtained through the iterative method have been analytically evaluated and presented in the form of a table and graph. The analytical solutions of these equations have been given in terms of convergent series with a simply calculable system, and the nonlinear terms in equations can easily be solved by the iterative method. Illustrative examples are also provided to demonstrate the applicability and efficiency of the method. The result renders the applicability and efficiency of the applied method. Finally, the quadruple Laplace transform and iterative method is an excellent method for the solution of nonlinear Klein-Gordon equations.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49388294","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 Modelling of the Spatial Epidemiology of COVID-19 with Different Diffusion Coefficients","authors":"B. Barnes, I. Takyi, Bright Emmanuel Owusu, Francis Ohene Boateng, Augustine Saahene, Emmanuel Saarah Baidoo, Jennifer Aduko Adombire","doi":"10.1155/2022/7563111","DOIUrl":"https://doi.org/10.1155/2022/7563111","url":null,"abstract":"This paper addresses the discrepancy between model findings and field data obtained and how it is minimized using the binning smoothing techniques: means, medians, and boundaries. Employing both the quantitative and the qualitative methods to examine the complex pattern involved in COVID-19 transmission dynamics reveals model variation and provides a boundary signature for the potential of the disease’s future spread across the country. To better understand the main underlying factor responsible for the epidemiology of COVID-19 infection in Ghana, the continuous inflow of foreigners, both with and without the disease, was incorporated into the classical Susceptible-Exposed-Quarantined-Recovered \u0000 \u0000 \u0000 \u0000 SEIQR\u0000 \u0000 \u0000 \u0000 model, which revealed the spread of the COVID-19 by these foreigners. Also, the diffusion model provided therein gives a threshold condition for the spatial spread of the COVID-19 infection in Ghana. Following the introduction of a new method for the construction of the Lyapunov function for global stability of the nonlinear system of ODEs was observed, overcoming the problem of guessing for the Lyapunov function.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45381430","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":"Applications of Two Methods in Exact Wave Solutions in the Space-Time Fractional Drinfeld–Sokolov–Wilson System","authors":"Elahe Miri Eskandari, N. Taghizadeh","doi":"10.1155/2022/4470344","DOIUrl":"https://doi.org/10.1155/2022/4470344","url":null,"abstract":"The fractional differential equations (FDEs) are ubiquitous in mathematically oriented scientific fields, such as physics and engineering. Therefore, FDEs have been the focus of many studies due to their frequent appearance in several applications such as physics, engineering, signal processing, systems identification, sound, heat, diffusion, electrostatics and fluid mechanics, and other sciences. The perusal of these nonlinear physical models through wave solutions analysis, corresponding to their FDEs, has a dynamic role in applied sciences. In this paper, the exp-function method and the rational \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 \u0000 G\u0000 \u0000 \u0000 ′\u0000 \u0000 \u0000 /\u0000 G\u0000 \u0000 \u0000 \u0000 \u0000 -expansion method are presented to establish the exact wave solutions of the space-time fractional Drinfeld–Sokolov–Wilson system in the sense of the conformable fractional derivative. The fractional Drinfeld–Sokolov–Wilson system contains fractional derivatives of the unknown function in terms of all independent variables. This system describes the shallow water wave models in fluid mechanics. These presented methods are a powerful mathematical tool for solving nonlinear conformable fractional evolution equations in various fields of applied sciences, especially in physics.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42804295","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":"On <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msub>\u0000 <mi>Λ</mi>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mi>B</mi>\u0000 ","authors":"J. Ereú, L. Pérez, Luz Rodríguez","doi":"10.1155/2022/5482688","DOIUrl":"https://doi.org/10.1155/2022/5482688","url":null,"abstract":"<jats:p>In this paper, we define the space of functions <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <msub>\u0000 <mi mathvariant=\"normal\">Λ</mi>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 </math>\u0000 </jats:inline-formula>-bounded variation on the plane and endow it with a norm under which it is a Banach space. In addition, we study some nonlinear integral equations and providing conditions for the functions and kernel involved in such equations under which we guarantee the existence and uniqueness in the space of functions of bounded variation in the sense of Shiba on the plane, <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <msub>\u0000 <mi mathvariant=\"normal\">Λ</mi>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mi>B</mi>\u0000 <mi>V</mi>\u0000 <mfenced open=\"(\" close=\")\" separators=\"|\">\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>I</mi>\u0000 <mi>a</mi>\u0000 <mi>b</mi>\u0000 </msubsup>\u0000 <mo>,</mo>\u0000 <mi>ℝ</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula>.</jats:p>","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"74 8","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41304499","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":"Oscillation of Fourth-Order Nonlinear Homogeneous Neutral Difference Equation","authors":"G. Sumitha, R. Kodeeswaran, S. Noeiaghdam, S. Balamuralitharan, V. Govindan","doi":"10.1155/2022/2406736","DOIUrl":"https://doi.org/10.1155/2022/2406736","url":null,"abstract":"In this paper, we establish the solution of the fourth-order nonlinear homogeneous neutral functional difference equation. Moreover, we study the new oscillation criteria have been established which generalize some of the existing results of the fourth-order nonlinear homogeneous neutral functional difference equation in the literature. Likewise, a few models are given to represent the significance of the primary outcomes.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41937534","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 Solutions for the Equal Width Equations Containing Generalized Fractional Derivative Using the Efficient Combined Method","authors":"M. Derakhshan","doi":"10.1155/2021/7066398","DOIUrl":"https://doi.org/10.1155/2021/7066398","url":null,"abstract":"&lt;jats:p&gt;In this paper, the efficient combined method based on the homotopy perturbation Sadik transform method  (HPSTM) is applied to solve the physical and functional equations containing the Caputo–Prabhakar fractional derivative. The mathematical model of this equation of order &lt;jats:inline-formula&gt;\u0000 &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mfenced open=\"(\" close=\"]\" separators=\"|\"&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0,1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/math&gt;\u0000 &lt;/jats:inline-formula&gt; with &lt;jats:inline-formula&gt;\u0000 &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℤ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;θ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;σ&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ℝ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/math&gt;\u0000 &lt;/jats:inline-formula&gt; is presented as follows: &lt;jats:inline-formula&gt;\u0000 &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"&gt;\u0000 &lt;mmultiscripts&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mstyle displaystyle=\"true\"&gt;\u0000 &lt;mi mathvariant=\"fraktur\"&gt;D&lt;/mi&gt;\u0000 &lt;/mstyle&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mprescripts /&gt;\u0000 &lt;none /&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;/mmultiscripts&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mfenced open=\"(\" close=\")\" separators=\"|\"&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;θ&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2021-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46073124","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 Method Based on Series Solution for Identifying an Unknown Source Coefficient on the Temperature Field in the Quasiperiodic Media","authors":"Bingxian Wang, C. Bai, M. Xu, L. Zhang","doi":"10.1155/2021/2893299","DOIUrl":"https://doi.org/10.1155/2021/2893299","url":null,"abstract":"In this paper, we consider the reconstruction of heat field in one-dimensional quasiperiodic media with an unknown source from the interior measurement. The innovation of this paper is solving the inverse problem by means of two different homotopy iteration processes. The first kind of homotopy iteration process is not convergent. For the second kind of homotopy iteration process, a convergent result is proved. Based on the uniqueness of this inverse problem and convergence results of the second kind of homotopy iteration process with exact data, the results of two numerical examples show that the proposed method is efficient, and the error of the inversion solution \u0000 \u0000 r\u0000 \u0000 \u0000 t\u0000 \u0000 \u0000 \u0000 is given.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2021-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45283393","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":"Electric Transverse Emissivity of Sinusoidal Surfaces Determined by a Differential Method: Comparison with Approximation of Geometric Optics","authors":"Taoufik Ghabara","doi":"10.1155/2021/1506485","DOIUrl":"https://doi.org/10.1155/2021/1506485","url":null,"abstract":"We present in this paper a numerical study of the validity limit of the optics geometrical approximation in comparison with a differential method which is established according to rigorous formalisms based on the electromagnetic theory. The precedent studies show that this method is adopted to the study of diffraction by periodic rough surfaces. For periods much larger than the wavelength, the mechanism is analog to what happens in a cavity where a ray is trapped and undergoes a large number of reflections. For gratings with a period much smaller than the wavelength, the roughness essentially behaves as a transition layer with a gradient of the optical index. Such a layer reduces the reflection there by increasing the absorption. The code has been implemented for TE polarization. We determine by the two methods such as differential method and the optics geometrical approximation the emissivity of gold and tungsten cylindrical surfaces with a sinusoidal profile, for a wavelength equal to 0.55 microns. The obtained results for a fixed height of the grating allowed us to delimit the validity domain of the optic geometrical approximation for the treated cases. The emissivity calculated by the differential method and that given on the basis of the homogenization theory are satisfactory when the period is much smaller than the wavelength.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2021-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46817935","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}