## 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
$D^{\alpha}u(t)= f(t,u), \quad t\in (0,T], \qquad t^{1-\alpha}u(t)\mid_{t=0} = u_ 0,$ where $$0<T<+\infty$$ and $$D^{\alpha}$$ is the Riemann-Liouville fractional derivative of order $$0<\alpha<1$$ is established and discussed.

### MSC:

 26A33 Fractional derivatives and integrals 34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations 34A40 Differential inequalities involving functions of a single real variable 34A99 General theory for ordinary differential equations
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### References:

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