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Fundamental solutions for semidiscrete evolution equations via Banach algebras. 半离散演化方程的Banach代数基本解。
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-01-07 DOI: 10.1186/s13662-020-03206-7
Jorge González-Camus, Carlos Lizama, Pedro J Miana
{"title":"Fundamental solutions for semidiscrete evolution equations via Banach algebras.","authors":"Jorge González-Camus,&nbsp;Carlos Lizama,&nbsp;Pedro J Miana","doi":"10.1186/s13662-020-03206-7","DOIUrl":"https://doi.org/10.1186/s13662-020-03206-7","url":null,"abstract":"<p><p>We give representations for solutions of time-fractional differential equations that involve operators on Lebesgue spaces of sequences defined by discrete convolutions involving kernels through the discrete Fourier transform. We consider finite difference operators of first and second orders, which are generators of uniformly continuous semigroups and cosine functions. We present the linear and algebraic structures (in particular, factorization properties) and their norms and spectra in the Lebesgue space of summable sequences. We identify fractional powers of these generators and apply to them the subordination principle. We also give some applications and consequences of our results.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"35"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-03206-7","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38814078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 11
Modeling of pressure-volume controlled artificial respiration with local derivatives. 用局部导数模拟压力-容积控制的人工呼吸。
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-01-14 DOI: 10.1186/s13662-020-03204-9
Bahar Acay, Mustafa Inc, Yu-Ming Chu, Bandar Almohsen
{"title":"Modeling of pressure-volume controlled artificial respiration with local derivatives.","authors":"Bahar Acay,&nbsp;Mustafa Inc,&nbsp;Yu-Ming Chu,&nbsp;Bandar Almohsen","doi":"10.1186/s13662-020-03204-9","DOIUrl":"https://doi.org/10.1186/s13662-020-03204-9","url":null,"abstract":"<p><p>We attempt to motivate utilization of some local derivatives of arbitrary orders in clinical medicine. For this purpose, we provide two efficient solution methods for various problems that occur in nature by employing the local proportional derivative defined by the proportional derivative (PD) controller. Under some necessary assumptions, a detailed exposition of the instantaneous volume in a lung is furnished by conformable derivative and such modified conformable derivatives as truncated <i>M</i>-derivative and proportional derivative. Moreover, we wish to investigate the performance of the above-mentioned operators in applications by plotting several graphs of the governing equations.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"49"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7807413/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38834140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis. 带分数导数的 SIR 流行病系统 (COVID-19) 数学模型：稳定性与数值分析。
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-01-04 DOI: 10.1186/s13662-020-03192-w
Rubayyi T Alqahtani
{"title":"Mathematical model of SIR epidemic system (COVID-19) with fractional derivative: stability and numerical analysis.","authors":"Rubayyi T Alqahtani","doi":"10.1186/s13662-020-03192-w","DOIUrl":"10.1186/s13662-020-03192-w","url":null,"abstract":"<p><p>In this paper, we study and analyze the susceptible-infectious-removed (SIR) dynamics considering the effect of health system. We consider a general incidence rate function and the recovery rate as functions of the number of hospital beds. We prove the existence, uniqueness, and boundedness of the model. We investigate all possible steady-state solutions of the model and their stability. The analysis shows that the free steady state is locally stable when the basic reproduction number  <math><msub><mi>R</mi> <mn>0</mn></msub> </math> is less than unity and unstable when <math><msub><mi>R</mi> <mn>0</mn></msub> <mo>></mo> <mn>1</mn></math> . The analysis shows that the phenomenon of backward bifurcation occurs when <math><msub><mi>R</mi> <mn>0</mn></msub> <mo><</mo> <mn>1</mn></math> . Then we investigate the model using the concept of fractional differential operator. Finally, we perform numerical simulations to illustrate the theoretical analysis and study the effect of the parameters on the model for various fractional orders.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"2"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7779337/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38804538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Higher order solitary solutions to the meta-model of diffusively coupled Lotka-Volterra systems. 扩散耦合Lotka-Volterra系统元模型的高阶孤立解。
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-02-25 DOI: 10.1186/s13662-021-03300-4
Inga Timofejeva, Tadas Telksnys, Zenonas Navickas, Romas Marcinkevicius, Minvydas Ragulskis
{"title":"Higher order solitary solutions to the meta-model of diffusively coupled Lotka-Volterra systems.","authors":"Inga Timofejeva,&nbsp;Tadas Telksnys,&nbsp;Zenonas Navickas,&nbsp;Romas Marcinkevicius,&nbsp;Minvydas Ragulskis","doi":"10.1186/s13662-021-03300-4","DOIUrl":"https://doi.org/10.1186/s13662-021-03300-4","url":null,"abstract":"<p><p>A meta-model of diffusively coupled Lotka-Volterra systems used to model various biomedical phenomena is considered in this paper. Necessary and sufficient conditions for the existence of <i>n</i>th order solitary solutions are derived via a modified inverse balancing technique. It is shown that as the highest possible solitary solution order <i>n</i> is increased, the number of nonzero solution parameter values remains constant for solitary solutions of order <math><mi>n</mi> <mo>></mo> <mn>3</mn></math> . Analytical and computational experiments are used to illustrate the obtained results.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"133"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-021-03300-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25419998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
∗-fuzzy measure model for COVID-19 disease. COVID-19疾病的模糊度量模型。
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-04-12 DOI: 10.1186/s13662-021-03363-3
Abbas Ghaffari, Reza Saadati
{"title":"∗-fuzzy measure model for COVID-19 disease.","authors":"Abbas Ghaffari,&nbsp;Reza Saadati","doi":"10.1186/s13662-021-03363-3","DOIUrl":"https://doi.org/10.1186/s13662-021-03363-3","url":null,"abstract":"<p><p>We introduce a mathematical model, namely, ∗-fuzzy measure model for COVID-19 disease and consider some properties of ∗-fuzzy measure such as Lebesque-Radon-Nikodym theorem.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"202"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-021-03363-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38814422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Dynamical system of the growth of COVID-19 with controller. 带有控制器的COVID-19生长动态系统。
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-01-07 DOI: 10.1186/s13662-020-03168-w
Rabha W Ibrahim, Dania Altulea, Rafida M Elobaid
{"title":"Dynamical system of the growth of COVID-19 with controller.","authors":"Rabha W Ibrahim,&nbsp;Dania Altulea,&nbsp;Rafida M Elobaid","doi":"10.1186/s13662-020-03168-w","DOIUrl":"https://doi.org/10.1186/s13662-020-03168-w","url":null,"abstract":"<p><p>Recently, various studied were presented to describe the population dynamic of covid-19. In this effort, we aim to introduce a different vitalization of the growth by using a controller term. Our method is based on the concept of conformable calculus, which involves this term. We investigate a system of coupled differential equations, which contains the dynamics of the diffusion among infected and asymptomatic characters. Strong control is considered due to the social separation. The result is consequently associated with a macroscopic law for the population. This dynamic system is useful to recognize the behavior of the growth rate of the infection and to confirm if its control is correctly functioning. A unique solution is studied under self-mapping properties. The periodicity of the solution is examined by using integral control and the optimal control is discussed in the sequel.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"9"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-03168-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38815546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Qualitative analysis of a two-group SVIR epidemic model with random effect. 具有随机效应的两组SVIR流行模型的定性分析。
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-03-19 DOI: 10.1186/s13662-021-03332-w
Kaiyan Zhao, Shaojuan Ma
{"title":"Qualitative analysis of a two-group SVIR epidemic model with random effect.","authors":"Kaiyan Zhao,&nbsp;Shaojuan Ma","doi":"10.1186/s13662-021-03332-w","DOIUrl":"https://doi.org/10.1186/s13662-021-03332-w","url":null,"abstract":"<p><p>In this paper, we investigate the dynamical behavior of a two-group SVIR epidemic model with random effect. Firstly, the two-group SVIR epidemic model with random perturbation of natural death rate is established. The existence and uniqueness of positive solution are proved by using stopping time theory and the Lyapunov analysis method. Secondly, a property of the system solution is obtained by using the law of strong numbers and the continuous local martingale. Finally, a new combination of Lyapunov functions is applied. The solution of the model we obtained is oscillating around a steady state if the basic reproduction number is less than one, which is the disease-free equilibrium of the corresponding deterministic model. A numerical simulation is presented to verify our theoretical results.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"172"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-021-03332-w","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25510454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Uniqueness of the Hadamard-type integral equations. hadamard型积分方程的唯一性。
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-01-09 DOI: 10.1186/s13662-020-03205-8
Chenkuan Li
{"title":"Uniqueness of the Hadamard-type integral equations.","authors":"Chenkuan Li","doi":"10.1186/s13662-020-03205-8","DOIUrl":"https://doi.org/10.1186/s13662-020-03205-8","url":null,"abstract":"<p><p>The goal of this paper is to study the uniqueness of solutions of several Hadamard-type integral equations and a related coupled system in Banach spaces. The results obtained are new and based on Babenko's approach and Banach's contraction principle. We also present several examples for illustration of the main theorems.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"40"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-020-03205-8","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38781390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen. 也门 COVID-19 和霍乱合并感染的动态优化控制模型。
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-02-15 DOI: 10.1186/s13662-021-03271-6
Ibrahim M Hezam, Abdelaziz Foul, Adel Alrasheedi
{"title":"A dynamic optimal control model for COVID-19 and cholera co-infection in Yemen.","authors":"Ibrahim M Hezam, Abdelaziz Foul, Adel Alrasheedi","doi":"10.1186/s13662-021-03271-6","DOIUrl":"10.1186/s13662-021-03271-6","url":null,"abstract":"<p><p>In this work, we propose a new dynamic mathematical model framework governed by a system of differential equations that integrates both COVID-19 and cholera outbreaks. The estimations of the model parameters are based on the outbreaks of COVID-19 and cholera in Yemen from January 1, 2020 to May 30, 2020. Moreover, we present an optimal control model for minimizing both the number of infected people and the cost associated with each control. Four preventive measures are to be taken to control the outbreaks: social distancing, lockdown, the number of tests, and the number of chlorine water tablets (CWTs). Under the current conditions and resources available in Yemen, various policies are simulated to evaluate the optimal policy. The results obtained confirm that the policy of providing resources for the distribution of CWTs, providing sufficient resources for testing with an average social distancing, and quarantining of infected individuals has significant effects on flattening the epidemic curves.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"108"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7883970/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"25391282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe. 用随机和确定性方法建模和预测COVID-19的传播:非洲和欧洲。
IF 4.1 3区 数学
Advances in Difference Equations Pub Date : 2021-01-01 Epub Date: 2021-01-20 DOI: 10.1186/s13662-021-03213-2
Abdon Atangana, Seda İğret Araz
{"title":"Modeling and forecasting the spread of COVID-19 with stochastic and deterministic approaches: Africa and Europe.","authors":"Abdon Atangana,&nbsp;Seda İğret Araz","doi":"10.1186/s13662-021-03213-2","DOIUrl":"https://doi.org/10.1186/s13662-021-03213-2","url":null,"abstract":"<p><p>Using the existing collected data from European and African countries, we present a statistical analysis of forecast of the future number of daily deaths and infections up to 10 September 2020. We presented numerous statistical analyses of collected data from both continents using numerous existing statistical theories. Our predictions show the possibility of the second wave of spread in Europe in the worse scenario and an exponential growth in the number of infections in Africa. The projection of statistical analysis leads us to introducing an extended version of the well-blancmange function to further capture the spread with fractal properties. A mathematical model depicting the spread with nine sub-classes is considered, first converted to a stochastic system, where the existence and uniqueness are presented. Then the model is extended to the concept of nonlocal operators; due to nonlinearity, a modified numerical scheme is suggested and used to present numerical simulations. The suggested mathematical model is able to predict two to three waves of the spread in the near future.</p>","PeriodicalId":53311,"journal":{"name":"Advances in Difference Equations","volume":"2021 1","pages":"57"},"PeriodicalIF":4.1,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1186/s13662-021-03213-2","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38859676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 78
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