Impulsive fractional differential equations with nonlinear boundary conditions
نویسندگان
چکیده
منابع مشابه
Some existence results for impulsive nonlinear fractional differential equations with mixed boundary conditions
and Applied Analysis 3 Definition 2.1. The fractional arbitrary order integral of the function h ∈ L1 J, R of order α ∈ R is defined by I 0h t 1 Γ α ∫ t 0 t − s α−1h s ds, 2.1 where Γ · is the Euler gamma function. Definition 2.2. For a function h given on the interval J , Caputo fractional derivative of order α > 0 is defined by D α 0 h t 1 Γ n − α ∫ t 0 t − s n−α−1h n s ds, n α 1, 2.2 where t...
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and Applied Analysis 3 To prove the existence of solutions of problem 1.1 , we need the following fixed-point theorems. Theorem 2.2 see 51 . Let E be a Banach space. Assume that Ω is an open bounded subset of E with θ ∈ Ω and let T : Ω → E be a completely continuous operator such that ‖Tu‖ ≤ ‖u‖, ∀u ∈ ∂Ω. 2.3 Then T has a fixed point in Ω. Lemma 2.3 see 1 . For α > 0, the general solution of fr...
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ژورنال
عنوان ژورنال: Mathematical and Computer Modelling
سال: 2012
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2011.07.037