Analysis of Caputo impulsive fractional order differential equations with applications

TL;DR

This paper investigates the existence and uniqueness of solutions for Caputo impulsive fractional differential equations of order between 0 and 1, including applications to logistic models and equations with finite delay.

Contribution

It introduces new results on the existence and uniqueness of solutions for Caputo impulsive fractional differential equations, extending previous work with novel methods and examples.

Findings

Established existence and uniqueness results for Caputo impulsive fractional equations

Provided examples including impulsive logistic models and delayed equations

Extended the theory to include equations with finite delay

Abstract

We use Sadavoskii's fixed point method to investigate the existence and uniqueness of solutions of Caputo impulsive fractional differential equations of order \alpha between 0 and 1 with one example of impulsive logistic model and few other examples as well. We also discuss Caputo impulsive fractional differential equations with finite delay. The results proven are new and complement the existing one.