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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:
26A33Fractional derivatives and integrals (real functions)
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
34A40Differential inequalities (ODE)
34A99General theory of ODE
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References:
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