Department of Mathematics
Toronto Metropolitan University
Toronto, Ontario, M5B 2K3, Canada
email: klan@torontomu.ca
Kunquan Lan
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.
DOI: 10.58997/ejde.2024.81
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Kunquan Lan Department of Mathematics Toronto Metropolitan University Toronto, Ontario, M5B 2K3, Canada email: klan@torontomu.ca |
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