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<p>In this article, we discuss existence theorems for a class of fractional differential equations without compactness or equicontinuity. The main conclusions are derived by exploiting a novel fixed point theorem of convex power condensing operators and the tool of measure of noncompactness. As applications, we apply our theoretical results to the semilinear convection equations in which memory effect are considered. Our work essentially extends and improves some previous studies on fractional differential equations with compactness or equicontinuity.</p>

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Solvability of a class of fractional differential equations under nonequicontinuity and applications

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月23日

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  • Yuting Chen,
  • Zhenbin Fan,
  • Gang Li

摘要

In this article, we discuss existence theorems for a class of fractional differential equations without compactness or equicontinuity. The main conclusions are derived by exploiting a novel fixed point theorem of convex power condensing operators and the tool of measure of noncompactness. As applications, we apply our theoretical results to the semilinear convection equations in which memory effect are considered. Our work essentially extends and improves some previous studies on fractional differential equations with compactness or equicontinuity.