Analysis of some generalized ABC- fractional logistic models

TL;DR

This paper investigates generalized ABC-fractional logistic models using Caputo derivatives with Mittag-Leffler kernels, proving existence, uniqueness, and stability, supported by numerical examples.

Contribution

It introduces and analyzes modified quadratic and cubic logistic models with multi-parametered Mittag-Leffler kernels in the fractional calculus framework.

Findings

Existence and uniqueness of solutions are established.

Stability of the models is analyzed through perturbation of equilibrium points.

Numerical examples illustrate the theoretical results.

Abstract

In this article, some logistic models in the settings of Caputo fractional operators with multi-parametered Mittag-Leffer kernels (ABC) are studied. This study mainly focuses on modified quadratic and cubic logistic models in the presence of a Caputo type fractional derivative. Existence and uniqueness theorems are proved and stability analysis is discussed by perturbing the equilibrium points. Numerical illustrative examples are discussed for the studied models.