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Existence of Solutions for Fractional Evolution Equations with Infinite Delay and Almost Sectorial Operator

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  • Shanshan Li
  • Shuqin Zhang

Abstract

This paper discusses a class of semilinear fractional evolution equations with infinite delay and almost sectorial operator on infinite interval in Banach space. By using the properties of analytic semigroups and Schauder’s fixed-point theorem, this paper obtains the existence of mild solutions of the fractional evolution equation. Moreover, this paper also discusses the existence of mild solution when the analytic semigroup lacks compactness by Kuratowski measures of noncompactness and Darbo–Sadovskii fixed-point theorem.

Suggested Citation

  • Shanshan Li & Shuqin Zhang, 2020. "Existence of Solutions for Fractional Evolution Equations with Infinite Delay and Almost Sectorial Operator," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-10, October.
    • Handle: RePEc:hin:jnlmpe:8868200
    DOI: 10.1155/2020/8868200
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