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<p>We establish new convexity results for sequential fractional differences of Riemann-Liouville type when the parameters belong to subregions of the space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2625_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="132" /> </InlineMediaObject> <EquationSource Format="TEX">\(\Omega:=(0,1)\times(1,2)\)</EquationSource> </InlineEquation>. Our methods are based on the transference principle. To do so, we prove transference results between three apparently different definitions of fractional differences. Our results show that the convexity is independent of the sign of the first initial value in a given subregion of Ω.</p>

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Convexity analysis of sequential fractional difference operators via transference principle

  • 期刊论文

  • 发表日期：

    2025年8月18日

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  • Meraa Arab,
  • Christopher S. Goodrich,
  • Carlos Lizama,
  • Pshtiwan Othman Mohammed

摘要

We establish new convexity results for sequential fractional differences of Riemann-Liouville type when the parameters belong to subregions of the space \(\Omega:=(0,1)\times(1,2)\) . Our methods are based on the transference principle. To do so, we prove transference results between three apparently different definitions of fractional differences. Our results show that the convexity is independent of the sign of the first initial value in a given subregion of Ω.