Scholarlink

<p>In the present paper, we consider a nonlocal boundary-value problem for a specific kind of nonlinear fractional differential equations encapsulating a collective fractional derivative known as the <i>ψ</i>-Caputo fractional operator. The applied fractional operator generated by the kernel is of the following kind: <i>k</i>(<i>t, s</i>) = <i>ψ</i>(<i>t</i>) <i>− ψ</i>(<i>s</i>)<i>.</i> The existence of solutions of the above-mentioned equations is established by using Mönch’s fixed-point theorem combined with the technique of measuring noncompactness. In addition, we discuss the problem of stability within the scope of the Ulam–Hyers stability criteria for the main fractional system. Finally, an example is given to illustrate the viability of the reported results.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Existence Theory for ψ-Caputo Fractional Differential Equations

  • 期刊论文

  • 发表日期：

    2025年2月1日

查看全文
  • Nadhir Bendrici,
  • Abdelatif Boutiara,
  • Malika Boumedien-Zidani

摘要

In the present paper, we consider a nonlocal boundary-value problem for a specific kind of nonlinear fractional differential equations encapsulating a collective fractional derivative known as the ψ-Caputo fractional operator. The applied fractional operator generated by the kernel is of the following kind: k(t, s) = ψ(t) − ψ(s). The existence of solutions of the above-mentioned equations is established by using Mönch’s fixed-point theorem combined with the technique of measuring noncompactness. In addition, we discuss the problem of stability within the scope of the Ulam–Hyers stability criteria for the main fractional system. Finally, an example is given to illustrate the viability of the reported results.