Hector Carmenate | Searcharxiv

arXiv2026

A Generalized Transform Framework for a Nonlinear Model of Cancer Dynamics

This paper develops a generalized transform framework for a logistic--Allee tumor-growth model. The method combines a generalized Laplace transform, Adomian decomposition, Chebyshev--Pad\'e rational reconstruction, and a \(\mu\)-scaled generalized transform to obtain admissible semi-analytical approximations. Comparisons with experimental tumor-growth data show that the resulting compact representations are stable, admissible, and comparable in error to standard numerical reference solutions.

math.NA↗

arXiv2023

Generalized Bernoulli Differential Equation

In this paper we propose and solve a generalization of the Bernoulli Differential Equation, by means of a generalized fractional derivative. First we prove a generalization of Gronwall's inequality, which is useful for studying the stability of systems of fractional differential equations and we state results about the qualitative behavior of the trivial solution of the proposed equation. After that, we prove and state the main results about the solution of the generalized Bernoulli Differential Equation and also we give some examples that show the advantage of considering this fractional derivative approach. We also present a finite difference method as an alternative to the solution of the generalized Bernoulli equation and prove its validity by means of examples.

math.GM↗