Stieltjes differential equations with bounded-variation derivators and application to thermal stress in solar panels

Abstract

In this work we extend the theory of Stieltjes systems beyond the monotone case, establishing new chain rules, generalized versions of the Fundamental Theorem of Calculus, compactness tools for Peano-type results, and a $g$-exponential for explicit linear solutions. Continuity notions relative to vector-valued derivators further allow us to study everywhere differentiable solutions. As an application, we model thermal stress effects on solar panels and battery health, highlighting the practical value of non-monotone derivators.