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Initial Value Problems of Fractional Order with Fractional Impulsive Conditions

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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.

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  1. Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR, 72204, USA

    Nickolai Kosmatov

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Kosmatov, N. Initial Value Problems of Fractional Order with Fractional Impulsive Conditions. Results. Math. 63, 1289–1310 (2013). https://doi.org/10.1007/s00025-012-0269-3

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  • DOI: https://doi.org/10.1007/s00025-012-0269-3

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