A New Theory of Calculus Based on Riemann-Stieltjes Integral

Abstract: In this paper, we establish a new theory of calculus. Based on Riemann-Stieltjes integral, a new definition of derivative is obtained, and we study some important properties of this new calculus, such as product rule, quotient rule, chain rule, and fundamental theorem of calculus. In fact, our results are extensions of the results of ordinary calculus. Keywords: New theory of calculus, Riemann-Stieltjes integral, product rule, quotient rule, chain rule, fundamental theorem of calculus. Title: A New Theory of Calculus Based on Riemann-Stieltjes Integral Author: Chii-Huei Yu International Journal of Novel Research in Computer Science and Software Engineering ISSN 2394-7314 Vol. 12, Issue 1, January 2025 - April 2025 Page No: 37-43 Novelty Journals Website: www.noveltyjournals.com Published Date: 28-January-2025 DOI: https://doi.org/10.5281/zenodo.14753511 Paper Download Link (Source) https://www.noveltyjournals.com/upload/paper/A%20New%20Theory%20of%20Calculus%20Based%20on%20Riemann-Stieltjes%20Integral-28012025-2.pdf