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Research Article | Open Access

Pseudo-Stieltjes calculus: α−pseudo-differentiability, the pseudo-Stieltjes integrability and applications

Caiqin Wang1, Hongbin Xie1( ), Zengtai Gong2( )
Basic Course Teaching Department, Gansu Institute of Mechanical and Electrical Engineering, Tianshui 741001, China
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
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Abstract

In this paper, the concepts of the α−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-analysispseudo-differentiabilitypseudo-Stieltjes integrability

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Electronic Research Archive
Volume 32 Issue 11,
November 2024
Pages 6467-6480
DOI: 10.3934/era.2024302

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Cite this article:
Wang C, Xie H, Gong Z. Pseudo-Stieltjes calculus: α−pseudo-differentiability, the pseudo-Stieltjes integrability and applications. Electronic Research Archive, 2024, 32(11): 6467-6480. https://doi.org/10.3934/era.2024302

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Received: 27 August 2024
Revised: 03 November 2024
Accepted: 14 November 2024
Published: 27 November 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)