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Zbl 1178.34005
Mophou, G.M.; N'Guérékata, G.M.
On integral solutions of some nonlocal fractional differential equations with nondense domain.
(English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 10, A, 4668-4675 (2009). ISSN 0362-546X

Summary: We prove the existence and uniqueness of integral solution for some nondensely defined fractional semilinear differential equation with nonlocal conditions $$\cases D^q_tx(t)=Ax(t)+f(t,x(t)),\quad t\in[0,T],\\ x(0)+g(x)=x_0.\endcases$$ The results are obtained by means of fixed point methods. We also give some examples of such problems.
MSC 2000:
*34A08
34G20 Nonlinear ODE in abstract spaces

Keywords: Cauchy problem; fractional abstract differential equation; nonlocal conditions

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