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<p>In this paper, we investigate wave equations featuring memory term and fractional derivative damping order <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varpi (t)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ϖ</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> over time. Initially, we establish the system’s well-posedness through semigroup theory, ensuring the existence and uniqueness of solutions. Additionally, we demonstrate the strong stability of our system. Furthermore, leveraging some criteria, we prove the rate of energy decay for the solutions.</p>

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Existence and stabilization of the wave equation with past history and fractional damping controls

  • 期刊论文

  • 发表日期：

    2026年5月17日

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  • Younes Bidi,
  • Khaled Zennir,
  • Abderrahmane Beniani,
  • Papadopoulos Pericles

摘要

In this paper, we investigate wave equations featuring memory term and fractional derivative damping order \(\varpi (t)\) ϖ ( t ) over time. Initially, we establish the system’s well-posedness through semigroup theory, ensuring the existence and uniqueness of solutions. Additionally, we demonstrate the strong stability of our system. Furthermore, leveraging some criteria, we prove the rate of energy decay for the solutions.