Remarks on the paper”Existence results for a class of fractional order boundary value problems with integrable impulses”,

Ravi Agarwal, Snezhana Hristova, Donal O’Regan

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Abstract

The aim of this paper is to correct (and extend) the formula for the solution and the sufficient conditions for existence and uniqueness given in the paper”Existence results for a class of fractional order boundary value problems with integrable impulses”, Dyn. Cont., Discr. Imp. Sys., Ser. A: Math. Anal., 25 (2018) 267-285. We will consider both known approaches in the literature in the interpretation of solutions of fractional equations with impulses i.e. the case of an unchangeable lower limit of the Caputo fractional derivatives over the whole interval of study and the case of changed lower limits at each time point of jump are both considered. We study both cases since in the above cited paper it is not clear which one is used. The formula for solutions and existence results are provided for both approaches in the literature to non-instantaneous impulsive fractional differential equations.

Original languageEnglish
Pages (from-to)69-80
Number of pages12
JournalDynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
Volume27
Issue number1
Publication statusPublished - 2020

Keywords

  • Caputo fractional differential equations
  • Delays
  • Existence
  • Non-instantaneous impulses

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