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Abstract <p>In this paper, the inverse problems of determining the right-hand side in mixed-type equations are considered. In one part of the domain, the considered equation is the subdiffusion equation with a fractional derivative in the sense of Gerasimov–Caputo of the order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\rho\in(0,1]\)</EquationSource> <!--LobJMat2561007Dusanova-m1--> </InlineEquation> and in the other part—a wave equation with a ordinary derivative. The right-hand side of the equations has the form <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(f(x)\phi(t)\)</EquationSource> <!--LobJMat2561007Dusanova-m2--> </InlineEquation>. Two inverse problems are investigated: in the first problem the unknown is <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\phi(t)\)</EquationSource> <!--LobJMat2561007Dusanova-m3--> </InlineEquation> for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(t&gt;0\)</EquationSource> <!--LobJMat2561007Dusanova-m4--> </InlineEquation>, in the second—for <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(t&lt;0\)</EquationSource> <!--LobJMat2561007Dusanova-m5--> </InlineEquation>.</p>

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Inverse Problems for Mixed Type Equations with the Gerasimov–Caputo Fractional Derivative

  • 期刊论文

  • 发表日期：

    2025年11月1日

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  • U. Kh. Dusanova

摘要

Abstract

In this paper, the inverse problems of determining the right-hand side in mixed-type equations are considered. In one part of the domain, the considered equation is the subdiffusion equation with a fractional derivative in the sense of Gerasimov–Caputo of the order \(\rho\in(0,1]\) and in the other part—a wave equation with a ordinary derivative. The right-hand side of the equations has the form \(f(x)\phi(t)\) . Two inverse problems are investigated: in the first problem the unknown is \(\phi(t)\) for \(t>0\) , in the second—for \(t<0\) .