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<p>This paper investigates a nonlinear inverse boundary value problem for semilinear hyperbolic equations with fractional derivatives of order <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\alpha \in (1, 2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. We establish the existence of solutions to this inverse problem using Krasnoselskii’s fixed-point theorem. To regularize the inherent ill-posedness of the problem, we implement appropriate a-priori assumptions on the solution alongside Fourier truncation methods. Moreover, we obtain a stability estimate of logarithmic type. The theoretical findings are validated through numerical simulations.</p>

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Fourier truncation method for inverse boundary value problems involving \(\psi \)-fractional semilinear hyperbolic equations

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Khadija Oufkir,
  • Najat Chefnaj,
  • Abdellah Taqbibt,
  • M.’hamed El Omari

摘要

This paper investigates a nonlinear inverse boundary value problem for semilinear hyperbolic equations with fractional derivatives of order \(\alpha \in (1, 2)\) α ∈ ( 1 , 2 ) . We establish the existence of solutions to this inverse problem using Krasnoselskii’s fixed-point theorem. To regularize the inherent ill-posedness of the problem, we implement appropriate a-priori assumptions on the solution alongside Fourier truncation methods. Moreover, we obtain a stability estimate of logarithmic type. The theoretical findings are validated through numerical simulations.