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Impulsive Boundary Value Problems for Two Classes of Fractional Differential Equation with Two Different Caputo Fractional Derivatives

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Abstract

We consider the impulsive boundary value problems for two classes of fractional differential equations with two different Caputo fractional derivatives and generalized boundary value conditions. Natural formulae of a solution for these problems are introduced, which can be regarded as a novelty item. Some sufficient conditions for existence and uniqueness of the solutions to this nonlinear equations are established by applying well-known Banach’s contraction mapping principle, Laplace transforms and some skills of inequalities. Finally, an example is given to illustrate the effectiveness of our results.

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  1. Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, 650093, Yunnan, China

    Kaihong Zhao

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  1. Kaihong Zhao
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Zhao, K. Impulsive Boundary Value Problems for Two Classes of Fractional Differential Equation with Two Different Caputo Fractional Derivatives. Mediterr. J. Math. 13, 1033–1050 (2016). https://doi.org/10.1007/s00009-015-0536-0

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  • DOI: https://doi.org/10.1007/s00009-015-0536-0

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