Non-Instantaneous Impulses in Differential Equations by Ravi Agarwal Snezhana Hristova & Donal O’Regan

Author:Ravi Agarwal, Snezhana Hristova & Donal O’Regan
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Now we will prove some comparison results for non-instantaneous impulsive Caputo fractional differential equations. Keeping in mind the discussions in Section 2.4.1 about the two approaches to the solutions of NIFrDE (2.48) and the derivatives of Lyapunov functions we will use approach (A2 for NIFrDE) and both the Caputo fractional derivative and the Caputo fractional Dini derivative of Lyapunov functions.

We will use the following condition:

(H2.3.2.1) The function is such that the equation x = ϕ k (t, x, y) has a unique solution x = ψ k (t, y),  t ∈ [s k , t k+1] and .

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