Quantum calculus with respect to another function

被引：3

作者：

Kamsrisuk, Nattapong ^{[1
]}

Passary, Donny ^{[1
]}

Ntouyas, Sotiris K. ^{[2
]}

Tariboon, Jessada ^{[1
]}

机构：

[1] King Mongkuts Univ Technol North Bangkok, Fac Appl Sci, Intelligent & Nonlinear Dynam Innovat Res Ctr, Dept Math, Bangkok 10800, Thailand

[2] Univ Ioannina, Dept Math, Ioannina 45110, Greece

来源：

AIMS MATHEMATICS | 2024年 / 9卷 / 04期

关键词：

quantum calculus; quantum derivative; quantum integral; Hermite-Hadamard inequality; boundary value problem; existence; uniqueness; fixed point theorem; FRACTIONAL Q-INTEGRALS; EXISTENCE;

D O I：

10.3934/math.2024510

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we studied the generalizations of quantum calculus on finite intervals. We presented the new definitions of the quantum derivative and quantum integral of a function with respect to another function and studied their basic properties. We gave an application of these newly defined quantum calculi by obtaining a new Hermite -Hadamard inequality for a convex function. Moreover, an impulsive boundary value problem involving quantum derivative, with respect to another function, was studied via the Banach contraction mapping principle.

引用

页码：10446 / 10461

页数：16

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