Solutions of Bernoulli equations in the fractional setting

TL;DR

This paper introduces a series solution for Bernoulli equations with Caputo fractional derivatives and explores a fractional logistic equation with numerical simulations.

Contribution

It provides a novel series representation formula for fractional Bernoulli equations and extends to fractional logistic models with numerical analysis.

Findings

Derived a general series solution formula for fractional Bernoulli equations.

Applied the method to a fractional logistic equation and performed numerical simulations.

Abstract

We present a general series representation formula for the local solution of Bernoulli equation with Caputo fractional derivatives. We then focus on a generalization of the fractional logistic equation and we present some related numerical simulations.