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

Caiqin Wang; Hongbin Xie; Zengtai Gong; Caiqin Wang; Hongbin Xie; Zengtai Gong

doi:10.3934/era.2024302

Electronic Research Archive

2024, Volume 32, Issue 11: 6467-6480. doi: 10.3934/era.2024302

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

1.
Basic Course Teaching Department, Gansu Institute of Mechanical and Electrical Engineering, Tianshui 741001, China
2.
College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received: 27 August 2024 Revised: 03 November 2024 Accepted: 14 November 2024 Published: 27 November 2024

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.
- pseudo-analysis,
- pseudo-differentiability,
- pseudo-Stieltjes integrability
Citation: Caiqin Wang, Hongbin Xie, Zengtai Gong. Pseudo-Stieltjes calculus: $ \alpha- $pseudo-differentiability, the pseudo-Stieltjes integrability and applications[J]. Electronic Research Archive, 2024, 32(11): 6467-6480. doi: 10.3934/era.2024302

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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.

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