Scholarlink

<p>This paper investigates direct and inverse problems for the time-fractional wave equation with a Riemann–Liouville fractional differential operator. In the direct problem, the initial-boundary problem for this equation with nonlocal boundary conditions of the Ionkin type is considered. Using Riesz bases in the space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12215_2025_1246_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="25" /> </InlineMediaObject> <EquationSource Format="TEX">\( L_2,\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> the Fourier method and the generalized singular inequality of Gronwall type, existence and uniqueness theorems are obtained for the solution of the direct problem. In the inverse problem, the time-dependent coefficient is required with an integral overdetermination condition. For this, the inverse problem is reduced to an equivalent integral equation of the Volterra type. The existence and uniqueness of a solution are then proven using the Banach fixed-point theorem.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Inverse coefficient problem for the fractional wave equation with non-local initial-boundary and integral type overdetermination conditions

  • 期刊论文

  • 发表日期：

    2025年6月30日

查看全文
  • D. K. Durdiev,
  • T. R. Suyarov

摘要

This paper investigates direct and inverse problems for the time-fractional wave equation with a Riemann–Liouville fractional differential operator. In the direct problem, the initial-boundary problem for this equation with nonlocal boundary conditions of the Ionkin type is considered. Using Riesz bases in the space \( L_2,\) L 2 , the Fourier method and the generalized singular inequality of Gronwall type, existence and uniqueness theorems are obtained for the solution of the direct problem. In the inverse problem, the time-dependent coefficient is required with an integral overdetermination condition. For this, the inverse problem is reduced to an equivalent integral equation of the Volterra type. The existence and uniqueness of a solution are then proven using the Banach fixed-point theorem.