Stability Analysis for Conformable Non-instantaneous Impulsive Differential Equations

Abstract

In this article, we analyze a class of conformable non-instantaneous impulsive differential equations and obtain their solutions using the non-instantaneous impulsive Cauchy matrix. We derive a suitable formula for the solution of conformable nonhomogeneous linear non-instantaneous impulsive perturbed problems and we study its exponential stability. We also investigate nonlinear non-instantaneous impulsive equations and provide some conditions needed to establish existence and uniqueness of their solutions and then we present a result which guarantees Ulam–Hyers–Rassias stability. Finally, an example is given to illustrate the theory.

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Correspondence to JinRong Wang.

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This work is partially supported by the National Natural Science Foundation of China (11661016), Training Object of High Level and Innovative Talents of Guizhou Province ((2016)4006), Major Research Project of Innovative Group in Guizhou Education Department ([2018]012) and Guizhou Data Driven Modeling Learning and Optimization Innovation Team ([2020]5016).

Communicated by Majid Gazor.

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Ding, Y., O’Regan, D. & Wang, J. Stability Analysis for Conformable Non-instantaneous Impulsive Differential Equations. Bull. Iran. Math. Soc. (2021). https://doi.org/10.1007/s41980-021-00595-7

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Keywords

  • Conformable derivative
  • Non-instantaneous impulsive differential equations
  • Exponential stability
  • Ulam–Hyers–Rassias stability

Mathematics Subject Classification

  • 34A37
  • 34D20