$(\omega ,c)$-periodic solutions for a class of fractional integrodifferential equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-04-07 DOI:10.1186/s13661-023-01726-1

E. Alvarez, R. Grau, R. Meriño

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引用次数: 0

Abstract

Abstract In this paper we investigate the following fractional order in time integrodifferential problem $$ \mathbb{D}_{t}^{\alpha}u(t)+Au(t)=f \bigl(t,u(t) \bigr)+ \int _{-\infty}^{t} k(t-s)g \bigl(s,u(s) \bigr)\,ds, \quad t \in \mathbb{R}. $$ D t α u ( t ) + A u ( t ) = f ( t , u ( t ) ) + ∫ − ∞ t k ( t − s ) g ( s , u ( s ) ) d s , t ∈ R . Here, $\mathbb{D}_{t}^{\alpha}$ D t α is the Caputo derivative. We obtain results on the existence and uniqueness of $(\omega ,c)$ ( ω , c ) -periodic mild solutions assuming that − A generates an analytic semigroup on a Banach space X and f , g , and k satisfy suitable conditions. Finally, an interesting example that fits our framework is given.

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$(\，c)$-一类分数阶积分微分方程的周期解

摘要本文研究了时间积分微分问题$$ \mathbb{D}_{t}^{\alpha}u(t)+Au(t)=f \bigl(t,u(t) \bigr)+ \int _{-\infty}^{t} k(t-s)g \bigl(s,u(s) \bigr)\,ds, \quad t \in \mathbb{R}. $$ D t α u (t) + A u (t) = f (t, u (t)) +∫−∞t k (t - s) g (s, u (s)) D s, t∈R中的分数阶问题。这里，$\mathbb{D}_{t}^{\alpha}$ dt α是卡普托导数。假设−A在Banach空间X上生成解析半群，且f、g、k满足适当条件，得到$(\omega ,c)$ (ω， c) -周期温和解的存在唯一性。最后，给出了一个适合我们框架的有趣示例。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.