Journal
ADVANCES IN DIFFERENCE EQUATIONS
Volume -, Issue -, Pages -Publisher
SPRINGER
DOI: 10.1186/s13662-017-1376-y
Keywords
Caputo fractional derivative; implicit fractional differential equations; fractional integral; non-instantaneous impulses; Ulam-type stability; Diaz-Margolis's fixed point theorem
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Funding
- National Natural Science Foundation of China [11571378]
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In this paper, we investigate four different types of Ulam stability, i.e., Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability for a class of nonlinear implicit fractional differential equations with non-instantaneous integral impulses and nonlinear integral boundary condition. We also establish certain conditions for the existence and uniqueness of solutions for such a class of fractional differential equations using Caputo fractional derivative. The arguments are based on generalized Diaz-Margolis's fixed point theorem. We provide two examples, which shows the validity of our main results.
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