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On integral solutions of some nonlocal fractional differential equations with nondense domain. (English) Zbl 1178.34005
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.

34A08Fractional differential equations
34G20Nonlinear ODE in abstract spaces
Full Text: DOI
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