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<p>In this work, making use of the theory of resolvent operators, the fractional power of closed linear operators and fixed point theorems, we discuss the global existence, local existence, uniqueness and regularity of the so-called mild solutions, under the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12591_2025_743_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha\)</EquationSource> </InlineEquation>-norm, for some neutral partial functional integro-differential equation with infinite delay. We assume that the linear part of the considered system generates an analytic resolvent operator. We begin with nonlinear part supposed to be continuous and Lipschitzian and in a second time we drop down this hypothesis. In the end, an example is given to illustrate the obtained results.</p>

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Existence and Regularity of Mild Solutions, in the Alpha Norm, for Neutral Integro-Differential Evolution Equations with Infinite Delay

  • 期刊论文

  • 发表日期：

    2025年11月8日

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  • Boubacar Diao,
  • Mamadou Sy

摘要

In this work, making use of the theory of resolvent operators, the fractional power of closed linear operators and fixed point theorems, we discuss the global existence, local existence, uniqueness and regularity of the so-called mild solutions, under the \(\alpha\) -norm, for some neutral partial functional integro-differential equation with infinite delay. We assume that the linear part of the considered system generates an analytic resolvent operator. We begin with nonlinear part supposed to be continuous and Lipschitzian and in a second time we drop down this hypothesis. In the end, an example is given to illustrate the obtained results.