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<p>The present paper aims to establishing precise and computationally effective error estimates for the L1 approximation applied to the regularized <i>k</i>-Prabhakar derivative when acting on functions with <i>k</i>-Hölder continuity. The primary finding reveals that the discretization error correlates with the difference between the regularity exponent and the derivative’s order. Secondly, we present a linear approximation for the regularized <i>k</i>-Prabhakar derivative. When <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(k=1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, the operator reduces to the classical Prabhakar derivative and the results are new for this case. A straightforward derivation of this result is presented, and its sharpness is validated through numerical simulations.</p>

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L1 discretization error analysis for regularized k-Prabhakar derivatives in Hölder spaces

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • İlkay Onbaşı Elidemir,
  • Suzan Cival Buranay,
  • Mehmet Ali Özarslan

摘要

The present paper aims to establishing precise and computationally effective error estimates for the L1 approximation applied to the regularized k-Prabhakar derivative when acting on functions with k-Hölder continuity. The primary finding reveals that the discretization error correlates with the difference between the regularity exponent and the derivative’s order. Secondly, we present a linear approximation for the regularized k-Prabhakar derivative. When \(k=1\) k = 1 , the operator reduces to the classical Prabhakar derivative and the results are new for this case. A straightforward derivation of this result is presented, and its sharpness is validated through numerical simulations.