Pseudo-Stieltjes calculus: $ \alpha- $pseudo-differentiability, the pseudo-Stieltjes integrability and applications

Abstract

In this paper, the concepts of the $ \alpha- $pseudo-differentiability and the pseudo-Stieltjes integrability are proposed, and the corresponding transformation theorems and Newton–Leibniz formula are established. The obtained results provide a framework for analyzing nonlinear differential equations.

Keywords

• pseudo-analysis
• pseudo-differentiability
• pseudo-stieltjes integrability