论具有希尔费分式衍生物的方程的非局部问题

IF 0.8 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics Pub Date : 2024-07-19 DOI:10.1134/s1995080224600729

R. R. Ashurov, Yu. E. Fayziev, N. M. Tukhtaeva

{"title":"论具有希尔费分式衍生物的方程的非局部问题","authors":"R. R. Ashurov, Yu. E. Fayziev, N. M. Tukhtaeva","doi":"10.1134/s1995080224600729","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3>In the paper, we study the nonlocal problem for a fractional partial differential equation with the Hilfer derivative. The non-local boundary value problem, \\(D^{\\alpha,\\beta}u(t)+Au(t)=f(t)\\) (\\(0<\\alpha<1\\), \\(0\\leq\\beta\\leq 1\\) and \\(0<t\\leq T\\)), \\(I^{\\delta}u(t)=\\gamma I^{\\delta}u(+0)+\\varphi\\) (\\(\\gamma\\) is a constant), in an arbitrary separable Hilbert space H with the strongly positive self-adjoint operator \\(A\\), is considered. In addition to the forward problem, the article also explores the inverse problem of determining the right-hand side of the equation. Existence and uniqueness theorems are proved to solve the forward and inverse problems.","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Nonlocal Problem for the Equation with the Hilfer Fractional Derivative\",\"authors\":\"R. R. Ashurov, Yu. E. Fayziev, N. M. Tukhtaeva\",\"doi\":\"10.1134/s1995080224600729\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3>In the paper, we study the nonlocal problem for a fractional partial differential equation with the Hilfer derivative. The non-local boundary value problem, \\\\(D^{\\\\alpha,\\\\beta}u(t)+Au(t)=f(t)\\\\) (\\\\(0<\\\\alpha<1\\\\), \\\\(0\\\\leq\\\\beta\\\\leq 1\\\\) and \\\\(0<t\\\\leq T\\\\)), \\\\(I^{\\\\delta}u(t)=\\\\gamma I^{\\\\delta}u(+0)+\\\\varphi\\\\) (\\\\(\\\\gamma\\\\) is a constant), in an arbitrary separable Hilbert space H with the strongly positive self-adjoint operator \\\\(A\\\\), is considered. In addition to the forward problem, the article also explores the inverse problem of determining the right-hand side of the equation. Existence and uniqueness theorems are proved to solve the forward and inverse problems.\",\"PeriodicalId\":46135,\"journal\":{\"name\":\"Lobachevskii Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-07-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Lobachevskii Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1134/s1995080224600729\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995080224600729","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

摘要本文研究了具有希尔费导数的分数偏微分方程的非局部问题。非局部边界值问题，(D^{\alpha,\beta}u(t)+Au(t)=f(t)\) (（0<\alpha<1\), （0\leq\beta\leq 1\) and\(0<；tleq T\)), \(I^{\delta}u(t)=\gamma I^{\delta}u(+0)+\varphi\) （（\(\gamma\)是一个常数），在一个任意可分离的希尔伯特空间H中与强正自相加算子\(A\)一起被考虑。除了正向问题，文章还探讨了确定方程右边的反向问题。证明了求解正向和反向问题的存在性和唯一性定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On the Nonlocal Problem for the Equation with the Hilfer Fractional Derivative

Abstract

In the paper, we study the nonlocal problem for a fractional partial differential equation with the Hilfer derivative. The non-local boundary value problem, \(D^{\alpha,\beta}u(t)+Au(t)=f(t)\) (\(0<\alpha<1\), \(0\leq\beta\leq 1\) and \(0<t\leq T\)), \(I^{\delta}u(t)=\gamma I^{\delta}u(+0)+\varphi\) (\(\gamma\) is a constant), in an arbitrary separable Hilbert space H with the strongly positive self-adjoint operator \(A\), is considered. In addition to the forward problem, the article also explores the inverse problem of determining the right-hand side of the equation. Existence and uniqueness theorems are proved to solve the forward and inverse problems.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

CiteScore

1.50

自引率

42.90%

发文量

127

期刊介绍： Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.