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Zbl 1178.26006
Agarwal, Ravi P.; Benchohra, Mouffak; Slimani, Boualem Attou
Existence results for differential equations with fractional order and impulses. (English)
[J] Mem. Differ. Equ. Math. Phys. 44, 1-21 (2008). ISSN 1512-0015

The authors study the fractional differential equation $$D^\alpha y(t)=f(t,y), \ \ t\in [0,T], \ \ 1<\alpha\le 2$$ where $D^\alpha y$ is the Caputo fractional derivative, in the setting where $y(t)$ is allowed to have jumps at a given set $\{t_1,...,t_m\}\subset [0,T]$. They prove three versions of the existence and uniqueness theorem for this equation under the initial conditions $y(0)=y_0, y^\prime(0)=y_1$, and a set of conditions on jumps of $y(t)$ and $y^\prime(t)$ at the points $t_1,...,t_m.$
[Stefan G. Samko (Faro)]

MSC 2000:: *26A33 Fractional derivatives and integrals (real functions)

Keywords: fractional differential equation; Caputo fractional derivative

Cited in: Zbl 1247.34004

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