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Monotone iterative method for initial value problem involving Riemann-Liouville fractional derivatives. (English) Zbl 1172.26307
By employing the method of monotone iteration, a result on the existence and uniqueness of a solution of the initial value problem for fractional differential equation $$D\sp{\alpha}u(t)= f(t,u), \quad t\in (0,T], \qquad t\sp{1-\alpha}u(t)\mid\sb{t=0} = u\sb 0,$$ where $0<T<+\infty$ and $D\sp{\alpha}$ is the Riemann-Liouville fractional derivative of order $0<\alpha<1$ is established and discussed.

##### MSC:
 26A33 Fractional derivatives and integrals (real functions) 34A12 Initial value problems for ODE, existence, uniqueness, etc. of solutions 34A40 Differential inequalities (ODE) 34A99 General theory of ODE
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##### References:
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