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<p>In this article, we establish the existence and uniqueness of a novel mathematical model aimed at image denoising. Our model integrates the fractional Laplacian operator, inspired by the Weickert filter, and employs the time Caputo fractional derivative. Through a rigorous analysis utilizing the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(H^{-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>H</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> </math></EquationSource> </InlineEquation> norm decomposition strategy, we present a system of coupled partial differential equations governing the evolution of a denoised image (<i>u</i>) and an associated residual (<i>v</i>) in space and time. Through this exploration, we aim to advance understanding and applications of time-fractional models in addressing challenges in image denoising and related fields.</p>

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Well-posedness for an improved time-fractional reaction-diffusion systems

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Ziad Zaabouli,
  • Lekbir Afraites,
  • Aissam Hadri,
  • Amine Laghrib

摘要

In this article, we establish the existence and uniqueness of a novel mathematical model aimed at image denoising. Our model integrates the fractional Laplacian operator, inspired by the Weickert filter, and employs the time Caputo fractional derivative. Through a rigorous analysis utilizing the \(H^{-1}\) H - 1 norm decomposition strategy, we present a system of coupled partial differential equations governing the evolution of a denoised image (u) and an associated residual (v) in space and time. Through this exploration, we aim to advance understanding and applications of time-fractional models in addressing challenges in image denoising and related fields.