EXISTENCE AND UNIQUENESS OF GENERALIZED NORMAL SOLUTIONS TO FIRST ORDER FRACTIONAL DIFFERENTIAL EQUATIONS AND APPLICATIONS

. We study the existence and uniqueness of continuous generalized normal solutions to initial value problems of first order fractional differential equations. We use the Banach contraction principle and the Weissinger fixed point theorem to obtain our results. We assume that the absolute values of the nonlinearities have upper bound functions in a subspace of continuous functions. As an example, the results are applied to equations with nonlinearities arising in logistic type population models with heterogeneous environments, and to population models of Ricker type.