International Journal of Differential Equations最新文献

{"title":"Stability Results for Nonlinear Implicit ϑ-Caputo Fractional Differential Equations with Fractional Integral Boundary Conditions","authors":"I. Kaddoura, Yahia Awad","doi":"10.1155/2023/5561399","DOIUrl":"https://doi.org/10.1155/2023/5561399","url":null,"abstract":"This article examines the necessary conditions for the unique existence of solutions to nonlinear implicit ϑ-Caputo fractional differential equations accompanied by fractional order integral boundary conditions. The analysis draws upon Banach’s contraction principle and Krasnoselskii’s fixed point theorem. Furthermore, the circumstances leading to the attainment of Ulam–Hyers–Rassias forms of stability are established. An illustrative example is provided to demonstrate the derived findings.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"115 3","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139133377","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":"Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis","authors":"N. B. Sharmila, C. Gunasundari, Mohammad Sajid","doi":"10.1155/2023/9190167","DOIUrl":"https://doi.org/10.1155/2023/9190167","url":null,"abstract":"In the realm of ecology, species naturally strive to enhance their own survival odds. This study introduces and investigates a predator-prey model incorporating reaction-diffusion through a system of differential equations. We scrutinize how diffusion impacts the model’s stability. By analysing the stability of the model’s uniform equilibrium state, we identify a condition leading to Turing instability. The study delves into how diffusion influences pattern formation within a predator-prey system. Our findings reveal that various spatiotemporal patterns, such as patches, spots, and even chaos, emerge based on species diffusion rates. We derive the amplitude equation by employing the weak nonlinear multiple scales analysis technique and the Taylor series expansion. A novel sinc interpolation approach is introduced. Numerical simulations elucidate the interplay between diffusion and Turing parameters. In a two-dimensional domain, spatial pattern analysis illustrates population density dynamics resulting in isolated groups, spots, stripes, or labyrinthine patterns. Simulation results underscore the method’s effectiveness. The article concludes by discussing the biological implications of these outcomes.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294780","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 MHD Carreau Nanofluid Flow with Nonlinear Thermal Radiation and Joule Heating by Employing Darcy–Forchheimer Effect over a Stretching Porous Medium","authors":"Endale Ersino Bafe, Mitiku Daba Firdi, Lemi Guta Enyadene","doi":"10.1155/2023/5495140","DOIUrl":"https://doi.org/10.1155/2023/5495140","url":null,"abstract":"Heat transfer in fluid mechanisms has a stronghold in everyday activities. To this end, nanofluids take a leading position in the advent of the betterment of thermal conductivity. The present study examines numerical investigations of incompressible magnetohydrodynamic (MHD) flow of Carreau nanofluid by considering nonlinear thermal radiation, Joule heating, temperature-dependent heat source/sink, and chemical reactions with attached Brownian movement and thermophoresis above a stretching sheet that saturates the porous medium. Pertaining similarity assumptions are used to change the flow equations into tractable forms of higher order nonlinear ordinary differential equations (ODEs). The continuation technique is adopted in the MATLAB bvp4c package for the numerical outcomes. The velocity, temperature, and nanoparticle concentration distributions in contrast to the leading parameters are availed in graphical and tabular descriptions. Among the many outcomes, increasing the radiation parameter from 0.2 to 0.8 surged the heat transfer rate by <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"> <mn>47.78</mn> <mo>%</mo> </math> at n = 1.5 and lifted it only by <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\"> <mn>8.5</mn> <mo>%</mo> </math> at n = 0.5. By boosting the magnetic parameter from 0 to 1.5, respective <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\"> <mn>37.64</mn> <mo>%</mo> </math> and <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M4\"> <mn>20.17</mn> <mo>%</mo> </math> rises in local drag forces are achieved in shear-thickening and thinning regions. On top of that, chemical reactions and Brownian motion parameters decay the concentration field. The distinctiveness of this method is that a solution is secured for the problem, which is highly sensitive to initial and boundary conditions. It will be worth mentioning that these fluid flow models will be applicable in various fields, such as engineering, petroleum, nuclear safety processes, and medical science.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"159 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135093530","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":"Cost-Effectiveness Analysis of the Optimal Control Strategies for Multidrug-Resistant Tuberculosis Transmission in Ethiopia","authors":"Ashenafi Kelemu Mengistu, Peter J. Witbooi","doi":"10.1155/2023/8822433","DOIUrl":"https://doi.org/10.1155/2023/8822433","url":null,"abstract":"Despite the recent progress of global control efforts, tuberculosis (TB) remains a significant public health threat worldwide, especially in developing countries, including Ethiopia. Furthermore, the emergence of multidrug-resistant tuberculosis (MDR-TB) has further complicated the situation. This study aims at identifying the most effective strategies for combating MDR-TB in Ethiopia. We first present a compartmental model of MDR-TB transmission dynamics in Ethiopia. The model is shown to have positive solutions, and the stability of the equilibrium points is analyzed. Then, we extend the model by incorporating time-dependent control variables. These control variables are vaccination, distancing, and treatment for DS-TB and MDR-TB. Finally, the optimality system is numerically simulated by considering different combinations of the strategies, and their cost effectiveness is analysed. Our finding shows that, among single control strategies, the successful treatment of drug-susceptible tuberculosis (DS-TB) is the most effective control factor for eliminating MDR-TB transmission in Ethiopia. Furthermore, within the six dual control strategies, the combination of distancing and successful treatment of DS-TB is less costly and more effective than other strategies. Finally, out of the triple control strategies, the combination of distancing, successful treatment for DS-TB, and treatment for MDR-TB is the most efficient strategy for curbing the MDR-TB disease in Ethiopia. Thus, to reduce MDR-TB efficiently, it is recommended that authorities focus on treating MDR-TB, effective treatment of DS-TB, and promoting social distancing through public health education and awareness programs.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135344980","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":"Group Analysis Explicit Power Series Solutions and Conservation Laws of the Time-Fractional Generalized Foam Drainage Equation","authors":"Maria Ihsane El Bahi, K. Hilal","doi":"10.1155/2023/8241804","DOIUrl":"https://doi.org/10.1155/2023/8241804","url":null,"abstract":"In this study, the classical Lie symmetry method is successfully applied to investigate the symmetries of the time-fractional generalized foam drainage equation with the Riemann–Liouville derivative. With the help of the obtained Lie point symmetries, the equation is reduced to nonlinear fractional ordinary differential equations (NLFODEs) which contain the Erdélyi–Kober fractional differential operator. The equation is also studied by applying the power series method, which enables us to obtain extra solutions. The obtained power series solution is further examined for convergence. Conservation laws for this equation are obtained with the aid of the new conservation theorem and the fractional generalization of the Noether operators.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64800183","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 Stabilizability of Nonbilinear Perturbed Descriptor Systems","authors":"Ghazwa F. Abd","doi":"10.1155/2023/5561224","DOIUrl":"https://doi.org/10.1155/2023/5561224","url":null,"abstract":"One way in which nonlinear descriptor systems of (index-k) naturally arise is through semiexplicit differential-algebraic equations. The study considers the nonbilinear dynamical systems which are described by the class of higher-index differential-algebraic equations (DAEs). Their nature is analysed both quantitatively and qualitatively, and stability characteristics are presented for their solution. Higher-index differential-algebraic systems seem to show inherent shaky around their solution manifolds. The often use of logarithmic norms is for the estimation of stability and perturbation bounds in linear ordinary differential equations (ODEs). The question of how to apply the notation of logarithmic norms to nonlinear DAEs has long been an open question. Other problem extensions including nonlinear dynamics and nonbilinear DAEs need subtle modification of the logarithmic norms. The logarithmic norm is combined by conceptual focus with the finite-time stability criterion in order to treat nonbilinear DAEs with the aim of covering some unbounded operators. This means we obtain the perturbation bounds from differential inequalities for a norm by the use of the relationship between Dini derivatives and semi-inner products. A numerical result obtained when tested on the nonbilinear mechanical system with a larger scale showed that the method was highly efficient and accurate and particularly suitable for nonbilinear DAEs.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41578882","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 and Asymptotic Behavior of Three-Dimensional Third-Order Delay Systems","authors":"Ahmed Abdul Hasan Naeif, Hussain A. Mohamad","doi":"10.1155/2023/9939317","DOIUrl":"https://doi.org/10.1155/2023/9939317","url":null,"abstract":"In this paper, oscillation and asymptotic behavior of three-dimensional third-order delay systems are discussed. Some sufficient conditions are obtained to ensure that every solution of the system is either oscillatory or nonoscillatory and converges to zero or diverges as \u0000 \u0000 t\u0000 \u0000 goes to infinity. A special technique is adopted to include all possible cases for all nonoscillatory solutions (NOSs). The obtained results included illustrative examples.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42295606","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":"Solving the Fractional Schrödinger Equation with Singular Initial Data in the Extended Colombeau Algebra of Generalized Functions","authors":"Ali El Mfadel, S. Melliani, A. Taqbibt, M. Elomari","doi":"10.1155/2023/3493912","DOIUrl":"https://doi.org/10.1155/2023/3493912","url":null,"abstract":"&lt;jats:p&gt;This manuscript aims to highlight the existence and uniqueness results for the following Schrödinger problem in the extended Colombeau algebra of generalized functions. &lt;jats:inline-formula&gt;\u0000 &lt;math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\"&gt;\u0000 &lt;mfenced open=\"{\" close=\"\" separators=\"|\"&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtable class=\"smallmatrix\"&gt;\u0000 &lt;mtr&gt;\u0000 &lt;mtd&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;ı&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi mathvariant=\"fraktur\"&gt;u&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfenced open=\"(\" close=\")\" separators=\"|\"&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mo mathvariant=\"fraktur\"&gt;△&lt;/mo&gt;\u0000 &lt;mi mathvariant=\"fraktur\"&gt;u&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfenced open=\"(\" close=\")\" separators=\"|\"&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfenced&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;v&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfenced open=\"(\" close=\")\" separators=\"|\"&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 ","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44745289","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 the Existence and Stability of Bounded Solutions for Abstract Dynamic Equations on Time Scales","authors":"C. Duque, H. Leiva, R. Gallo, A. Tridane","doi":"10.1155/2023/8489196","DOIUrl":"https://doi.org/10.1155/2023/8489196","url":null,"abstract":"In this article we study the existence and stability of bounded solutions for semilinear abstract dynamic equations on time scales in Banach spaces. In order to do so, we use the definition of the Riemann delta-integral to prove a result about closed operator in Banach spaces and then we just use the representation of bounded solutions as an improper delta-integral from minus infinite to \u0000 \u0000 t\u0000 \u0000 . We prove the existence, uniqueness, and exponential stability of such bounded solutions. As particular cases, we study the existence of periodic and almost periodic solutions as well. Finally, we present some equations on time scales where our results can be applied.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-04-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46373733","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 of Renormalized Solution to Nonlinear Anisotropic Elliptic Problems with Variable Exponent and <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 <","authors":"Ibrahime Konaté, Arouna Ouédraogo","doi":"10.1155/2023/9454714","DOIUrl":"https://doi.org/10.1155/2023/9454714","url":null,"abstract":"Nonlinear partial differential equations are considered as an essential tool for describing the behavior of many natural phenomena. The modeling of some phenomena requires to work in Sobolev spaces with constant exponent. But for others, such as electrorheological fluids, the properties of classical spaces are not sufficient to have precision. To overcome this difficulty, we work in the appropriate spaces called Lebesgue and Sobolev spaces with variable exponent. In recent works, researchers are attracted by the study of mathematical problems in the context of variable exponent. This great interest is motivated by their applications in many fields such as elastic mechanics, fluid dynamics, and image restoration. In this paper, we combine the technic of monotone operators in Banach spaces and approximation methods to prove the existence of renormalized solutions of a class of nonlinear anisotropic problem involving \u0000 \u0000 \u0000 p\u0000 ⟶\u0000 \u0000 \u0000 \u0000 .\u0000 \u0000 \u0000 −\u0000 \u0000 Leray–Lions operator, a graph, and \u0000 \u0000 \u0000 \u0000 L\u0000 \u0000 \u0000 1\u0000 \u0000 \u0000 \u0000 data. In particular, we establish the uniqueness of the solution when the graph data are considered a strictly increasing function.","PeriodicalId":55967,"journal":{"name":"International Journal of Differential Equations","volume":" ","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48884709","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}