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<p>This paper investigates linear fractional-order wave equations with constant time delay. Initially, the analytic solution and regularity of the equation are analyzed. The symmetric fractional-order reduction (SFOR) method is then used to transform the original problem into an equivalent coupled system. Based on this, an Alikhanov scheme is developed in this paper. The stability and convergence of the proposed scheme are derived using the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H^2\)</EquationSource> </InlineEquation> energy method. Numerical experiments are conducted to validate the effectiveness of the theoretical results.</p>

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Order reduction technique combined with Alikhanov method for delay time-fractional wave equations

  • 期刊论文

  • 发表日期：

    2026年1月12日

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  • Yueyue Tan,
  • Caixia Ou,
  • Seakweng Vong

摘要

This paper investigates linear fractional-order wave equations with constant time delay. Initially, the analytic solution and regularity of the equation are analyzed. The symmetric fractional-order reduction (SFOR) method is then used to transform the original problem into an equivalent coupled system. Based on this, an Alikhanov scheme is developed in this paper. The stability and convergence of the proposed scheme are derived using the \(H^2\) energy method. Numerical experiments are conducted to validate the effectiveness of the theoretical results.