Electronic Journal of Differential Equations, Vol. 2024 (2024), No. 81, pp. 1-16.

Title: Existence and uniqueness of generalized normal solutions to first order fractional differential equations and applications

Author: Kunquan Lan (Toronto Metropolitan Univ., Toronto, Ontario, Canada)
  
Abstract:
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.

Submitted October 30, 2024. Published December 10, 2024.
Math Subject Classifications: 34A08, 26A33, 34A12, 45D05.
Key Words: First order fractional differential equation; initial value problem; 
  generalized normal solutions;  existence and uniqueness.