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<p>This paper is devoted to the continuity of the weak solution for tempered fractional general diffusion equations driven by tempered fractional Brownian motion (TFBM). Based on the Feynman-Kac formula (<InternalRef RefID="Equ2">1.2</InternalRef>), by using the Itô isometry for the stochastic integral with respect to TFBM, Parseval’s identity and some ingenious calculations, we establish the continuities of the solution with respect to Hurst index <i>H</i> and tempering parameter <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13540_2024_369_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation> of TFBM.</p>

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Continuity of solutions for tempered fractional general diffusion equations driven by TFBM

  • 期刊论文

  • 发表日期：

    2025年1月3日

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  • Lijuan Zhang,
  • Yejuan Wang

摘要

This paper is devoted to the continuity of the weak solution for tempered fractional general diffusion equations driven by tempered fractional Brownian motion (TFBM). Based on the Feynman-Kac formula (1.2), by using the Itô isometry for the stochastic integral with respect to TFBM, Parseval’s identity and some ingenious calculations, we establish the continuities of the solution with respect to Hurst index H and tempering parameter \(\lambda \) λ of TFBM.