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General solutions of higher order impulsive fractional differential equations involved with the Caputo type generalized fractional derivatives and applications

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Abstract

The generalized fractional integral operator and the Caputo type generalized fractional derivative operator are defined which contain the Riemann- Liouville integral operator, the Hadamard fractional integral operator, the Ca-puto fractional derivative operator and the Caputo type Hadamard fractional derivative operator as special cases. General solutions (the explicit solutions) of the impulsive Caputo type generalized fractional differential equations are given. Applying our results, existence results of solutions of boundary value problems for an impulsive fractional differential equations involved with the Caputo type generalized fractional derivatives are established. Examples and some remarks on recent published papers are presented to illustrate the main theorems.

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Authors and Affiliations

  1. Department of Mathematics, Guangdong University of Finance and Economics, Guangzhou, 510000, China

    Yuji Liu

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  1. Yuji Liu
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Correspondence to Yuji Liu.

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Communicated by L. Hatvani

Supported by National Natural Science Foundation of China (No: 11401111), the Natural Science Foundation of Guangdong province (No: S2011010001900) and the Foundation for High-level talents in Guangdong Higher Education Project.

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Liu, Y. General solutions of higher order impulsive fractional differential equations involved with the Caputo type generalized fractional derivatives and applications. ActaSci.Math. 83, 457–485 (2017). https://doi.org/10.14232/actasm-016-793-1

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  • DOI: https://doi.org/10.14232/actasm-016-793-1

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