On the concept and existence of solution for impulsive fractional differential equations

► Error is shown in former solutions for impulsive fractional differential equations. ► A correct solution is found for those impulsive Caputo fractional Cauchy problems. ► Some sufficient conditions are established for the existence of solutions. This paper is motivated from some recent papers trea...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2012-07, Vol.17 (7), p.3050-3060
Main Authors: Fec˘kan, Michal, Zhou, Yong, Wang, JinRong
Format: Article
Language:English
Subjects:
Caputo fractional derivative
Cauchy problem
Computer simulation
Derivatives
Differential equations
Existence
Impulsive differential equations
Mathematical models
Nonlinearity
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Summary:► Error is shown in former solutions for impulsive fractional differential equations. ► A correct solution is found for those impulsive Caputo fractional Cauchy problems. ► Some sufficient conditions are established for the existence of solutions. This paper is motivated from some recent papers treating the problem of the existence of a solution for impulsive differential equations with fractional derivative. We firstly show that the formula of solutions in cited papers are incorrect. Secondly, we reconsider a class of impulsive fractional differential equations and introduce a correct formula of solutions for a impulsive Cauchy problem with Caputo fractional derivative. Further, some sufficient conditions for existence of the solutions are established by applying fixed point methods. Some examples are given to illustrate the results.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2011.11.017