An Improved Version of the Classical Banister Model to Predict Changes in Physical Condition.

In this paper, we formulate and provide the solutions to two new models to predict changes in physical condition by using the information of the training load of an individual. The first model is based on a functional differential equation, and the second one on an integral differential equation. Both models are an extension to the classical Banister model and allow to overcome its main drawback: the variations in physical condition are influenced by the training loads of the previous days and not only of the same day. Finally, it is illustrated how the first model works with a real example of the training process of a cyclist.

Differential equations of arbitrary order under Caputo-Fabrizio derivative: some existence results and study of stability.

In this work, we consider the problem of the existence and uniqueness of solution, and also the simple existence of solution, for implicit differential equations of arbitrary order involving Caputo-Fabrizio derivative. The main tools for this study are contraction mapping principle and Schaefer's fixed point result. We also study the stability of the equations in the sense of Ulam-Hyers and also from the perspective of Ulam-Hyers-Rassias.