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Results in Mathematics

, Volume 63, Issue 3–4, pp 1289–1310 | Cite as

Initial Value Problems of Fractional Order with Fractional Impulsive Conditions

  • Nickolai KosmatovEmail author
Article

Abstract

In this paper we intend to accomplish two tasks firstly, we address some basic errors in several recent results involving impulsive fractional equations with the Caputo derivative, and, secondly, we study initial value problems for nonlinear differential equations with the Riemann–Liouville derivative of order 0 < α ≤ 1 and the Caputo derivatives of order 1 < δ < 2. In both cases, the corresponding fractional derivative of lower order is involved in the formulation of impulsive conditions.

Mathematics Subject Classification (2000)

34A08 34A37 

Keywords

Caputo derivative fixed point impulsive condition Riemann–Liouville derivative 

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© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Arkansas at Little RockLittle RockUSA

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