Quantum calculus with respect to another function

Nattapong Kamsrisuk; Donny Passary; Sotiris K. Ntouyas; Jessada Tariboon; Nattapong Kamsrisuk; Donny Passary; Sotiris K. Ntouyas; Jessada Tariboon

doi:10.3934/math.2024510

AIMS Mathematics

2024, Volume 9, Issue 4: 10446-10461. doi: 10.3934/math.2024510

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Research article

Quantum calculus with respect to another function

1.
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
2.
Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece

Received: 29 December 2023 Revised: 07 March 2024 Accepted: 12 March 2024 Published: 18 March 2024
MSC : 26D15, 34A08, 34B37

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.
- quantum calculus,
- quantum derivative,
- quantum integral,
- Hermite-Hadamard inequality,
- boundary value problem,
- existence,
- uniqueness,
- fixed point theorem
Citation: Nattapong Kamsrisuk, Donny Passary, Sotiris K. Ntouyas, Jessada Tariboon. Quantum calculus with respect to another function[J]. AIMS Mathematics, 2024, 9(4): 10446-10461. doi: 10.3934/math.2024510

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Abstract

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.

References

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