Studies on impulsive differential models with multi-term Riemann–Liouville fractional derivatives

Abstract

In this article, two impulsive models for fractional differential equations are proposed. By converting the impulsive fractional differential equations into integral equations technically, some existence results on solutions of two classes of initial value problems for nonlinear singular multi-term fractional differential models with impulses involving Riemann–Liouville fractional derivatives are established. The first one has a single base point and the second one has multiple base points. In both cases, the corresponding fractional derivative of lower order is involved in the fractional differential equations. Our results improve some known theorems see Remarks 4.1 and 5.1. Examples are presented to illustrate the main theorems. Finally we give a conclusions section in which some basic errors in a recent paper involving impulsive fractional equations with the Riemann–Liouville derivative are addressed, see Claim 7.1 and Remark 7.2.