On Generalized Fractional Operators and a Gronwall Type Inequality with Applications

Abstract

In this paper, we obtain the Gronwall type inequality for generalized fractional operators
unifying Riemann-Liouville and Hadamard fractional operators. We apply this inequality
to the dependence of the solution of dierential equations, involving generalized fractional
derivatives, on both the order and the initial conditions. More properties for the generalized
fractional operators are formulated and the solutions of initial value problems in certain new
weighted spaces of functions are established as well.