On a New Type $pq$-Calculus

TL;DR

This paper introduces a novel $pq$-calculus, exploring its derivatives and integrals, establishing fundamental theorems and integration by parts formulas to expand the mathematical framework.

Contribution

The paper presents the first comprehensive development of $pq$-calculus, including derivatives, integrals, and fundamental theorems, enhancing existing calculus theories.

Findings

Defined $pq$-derivative and $pq$-integral

Established fundamental theorem of $pq$-calculus

Derived formulas for $pq$-integration by parts

Abstract

In this paper, we introduce a new type of $ pq $-calculus. The $ pq $-derivative and $ pq $-integration are investigated and various properties of these concepts are given. The fundamental theorem of $ pq $-calculus and formulas of $ pq $-integration by part are also presented.