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
收藏
页码：10446 / 10461
页数：16
相关论文
共 50 条
  • [21] Nonlinear Piecewise Caputo Fractional Pantograph System with Respect to Another Function
    Abdo, Mohammed S. S.
    Shammakh, Wafa
    Alzumi, Hadeel Z. Z.
    Alghamd, Najla
    Albalwi, M. Daher
    FRACTAL AND FRACTIONAL, 2023, 7 (02)
  • [22] ON THE DEFINITION OF THE PARTITION-FUNCTION IN QUANTUM REGGE CALCULUS
    NISHIMURA, J
    PROGRESS OF THEORETICAL PHYSICS, 1995, 94 (02): : 299 - 304
  • [23] A note on a class of Caputo fractional differential equations with respect to another function
    Zaky, M. A.
    Hendy, A. S.
    Suragan, D.
    MATHEMATICS AND COMPUTERS IN SIMULATION, 2022, 196 : 289 - 295
  • [24] General fractional calculus with respect to exponential function used in fundamental viscoelastic models
    Feng, Yi-Ying
    Wang, Yi-Ming
    Xu, Xiu-Rong
    Li, Yao-Hong
    Wei, Zhang-Zhi
    Jin, Shou-Bo
    INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2024,
  • [25] Operational Calculus for the Riemann–Liouville Fractional Derivative with Respect to a Function and its Applications
    Hafiz Muhammad Fahad
    Arran Fernandez
    Fractional Calculus and Applied Analysis, 2021, 24 : 518 - 540
  • [26] On Fejer Type Inequalities for Convex Mappings Utilizing Fractional Integrals of a Function with Respect to Another Function
    Hüseyin Budak
    Results in Mathematics, 2019, 74
  • [27] On Fejer Type Inequalities for Convex Mappings Utilizing Fractional Integrals of a Function with Respect to Another Function
    Budak, Huseyin
    RESULTS IN MATHEMATICS, 2019, 74 (01)
  • [28] Impulsive boundary value problems containing Caputo fractional derivative of a function with respect to another function
    Chanon Promsakon
    Eakachai Suntonsinsoungvon
    Sotiris K. Ntouyas
    Jessada Tariboon
    Advances in Difference Equations, 2019
  • [29] Boundary value problem of weighted fractional derivative of a function with a respect to another function of variable order
    Kheireddine Benia
    Mohammed Said Souid
    Fahd Jarad
    Manar A. Alqudah
    Thabet Abdeljawad
    Journal of Inequalities and Applications, 2023
  • [30] On Hermite-Hadamard type inequalities via fractional integrals of a function with respect to another function
    Jleli, Mohamed
    Samet, Bessem
    JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2016, 9 (03): : 1252 - 1260
12345