2026 Volume 16 Issue 1
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Wenjie Liu, Shengli Xie. EXISTENCE RESULTS OF MILD SOLUTIONS FOR IMPULSIVE FRACTIONAL MEASURE DRIVEN DIFFERENTIAL EQUATIONS WITH INFINITE DELAY[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 188-208. doi: 10.11948/20240558
Citation: Wenjie Liu, Shengli Xie. EXISTENCE RESULTS OF MILD SOLUTIONS FOR IMPULSIVE FRACTIONAL MEASURE DRIVEN DIFFERENTIAL EQUATIONS WITH INFINITE DELAY[J]. Journal of Applied Analysis & Computation, 2026, 16(1): 188-208. doi: 10.11948/20240558

EXISTENCE RESULTS OF MILD SOLUTIONS FOR IMPULSIVE FRACTIONAL MEASURE DRIVEN DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

  • Author Bio: Email: slxie@ahjzu.edu.cn(S. Xie)
  • Corresponding author: Email: 2020035@cua.edu.cn(W. Liu) 
  • Fund Project: The authors were supported by Natural Science Foundation of Anhui Province (2023AH051433, 2024AH050885), Anhui Provincial Education Department (11040606M01) and the Key Project of Anhui Vocational and Technical College (2023yjjxyj37)
  • The primary focus of this study is the existence and uniqueness of mild solutions for impulsive fractional measure driven differential equations with infinite delay in regular function spaces. First, we rigorously justify the definition of mild solutions for impulsive fractional measure driven differential equations. Then, under conditions of semigroup noncompactness, by utilizing operator semigroup theory, the Kuratowski measure of noncompactness, fixed point theorems, and piecewise estimation techniques, sufficient conditions for the existence of mild solutions are derived. This work extends numerous prior research outcomes, eschewing the need for any priori estimates or noncompactness constraints. Finally, an illustrative example is provided to demonstrate the applicability and efficacy of the theoretical framework.

    MSC: 34B10, 34B16, 34A38, 34K37
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