Asymptotic behavior of solutions to nonlinear initial-value fractional differential problems

We study the boundedness and asymptotic behavior of solutions for a class of nonlinear fractional differential equations. These equations involve two Riemann-Liouville fractional derivatives of different orders. We determine fairly large classes of nonlinearities and appropriate underlying spaces where solutions are bounded, exist globally and decay to zero as a power type function. Our results are obtained by using generalized versions of Gronwall- Bellman inequality, appropriate regularization techniques and several properties of fractional derivatives. Three examples are given to illustrate our results.