Global existence of mild solutions for impulsive $ \psi- $Caputo fractional parabolic equations

Yonghong Ding; Yongxiang Li; Yonghong Ding; Yongxiang Li

doi:10.3934/era.2025190

Electronic Research Archive

2025, Volume 33, Issue 7: 4205-4221. doi: 10.3934/era.2025190

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Global existence of mild solutions for impulsive $ \psi- $Caputo fractional parabolic equations

Yonghong Ding ^{1
,
,},
Yongxiang Li ²

1.
Department of Mathematics, Tianshui Normal University, Tianshui 741000, China
2.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China

Received: 02 April 2025 Revised: 10 June 2025 Accepted: 26 June 2025 Published: 10 July 2025

This paper investigated a class of nonlinear $ \psi- $Caputo fractional parabolic equations with impulsive. We reformulated the fractional parabolic equations into abstract evolution equations. By using the nonlinear analysis method and fixed point theorems, we obtained the existence and uniqueness of the global of mild solutions for the problem.
- $ \psi- $Caputo fractional derivative,
- impulsive,
- global existence,
- mild solution
Citation: Yonghong Ding, Yongxiang Li. Global existence of mild solutions for impulsive $ \psi- $Caputo fractional parabolic equations[J]. Electronic Research Archive, 2025, 33(7): 4205-4221. doi: 10.3934/era.2025190

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Abstract

This paper investigated a class of nonlinear $ \psi- $Caputo fractional parabolic equations with impulsive. We reformulated the fractional parabolic equations into abstract evolution equations. By using the nonlinear analysis method and fixed point theorems, we obtained the existence and uniqueness of the global of mild solutions for the problem.

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