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Fractional problems with right-handed Riemann-Lioville fractional derivatives

Jankowski T.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2016

Vol. 20, No 1

63--83

In this paper, we investigate the existence of solutions for advanced fractional differential equations containing the right-handed Riemann-Liouville fractional derivative both with nonlinear boundary conditions and also with initial conditions given at the end point T of interval [0,T]. We use both the method of successive approximations, the Banach fixed point theorem and the monotone iterative technique, as well. Linear problems are also discussed. A few examples illustrate the results