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Zbl 1180.34006
Mophou, G.M.; N'Guérékata, G.M.
Existence of the mild solution for some fractional differential equations with nonlocal conditions.
(English)
[J] Semigroup Forum 79, No. 2, 315-322 (2009). ISSN 0037-1912

Summary: We are concerned in this paper with the existence of mild solutions to the Cauchy Problem for the fractional differential equation with nonlocal conditions: $$D^q x(t)= Ax(t)+ t^n f(t,x(t),Bx(t)), \quad t\in[0,T],\ n\in\Bbb Z^+,\ x(0)+g(x)=x_0,$$ where $0<q<1$, $A$ is the infinitesimal generator of a $C_0$-semigroup of bounded linear operators on a Banach space $X$.
MSC 2000:
*34A08
34G20 Nonlinear ODE in abstract spaces

Keywords: Cauchy problem; fractional abstract differential equation; nonlocal conditions; semigroup of bounded operators

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