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<p>This paper concentrates on the examination of a class of nonlocal initial value problems for Langevin fractional differential equations featuring the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10958_2025_7573_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\psi\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ψ</mi> </math></EquationSource> </InlineEquation>-Caputo fractional derivative within Banach spaces. By utilizing Banach’s fixed-point theorem, we establish the uniqueness of the solutions to these problems. The existence of solutions is then confirmed using Schaefer’s and Darbo’s fixed-point theorems. Finally, we provide examples to illustrate our findings.</p>

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A STUDY ON SOME CLASSES OF PANTOGRAPH LANGEVIN FRACTIONAL DIFFERENTIAL PROBLEMS WITH NONLOCAL CONDITIONS

  • 期刊论文

  • 发表日期：

    2025年3月19日

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  • Houari Bouzid,
  • Abdelkader Benali,
  • Abdelkrim Salim,
  • İnci M. Erhan

摘要

This paper concentrates on the examination of a class of nonlocal initial value problems for Langevin fractional differential equations featuring the \(\psi\) ψ -Caputo fractional derivative within Banach spaces. By utilizing Banach’s fixed-point theorem, we establish the uniqueness of the solutions to these problems. The existence of solutions is then confirmed using Schaefer’s and Darbo’s fixed-point theorems. Finally, we provide examples to illustrate our findings.