Quantum Laplace Transforms for the Ulam–Hyers Stability of Certain q-Difference Equations of the Caputo-like Type-Reference-Cited by-同舟云学术

Quantum Laplace Transforms for the Ulam–Hyers Stability of Certain q-Difference Equations of the Caputo-like Type

Published:2024-07-28 Issue:8 Volume:8 Page:443
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Etemad Sina¹^ORCID,Stamova Ivanka²^ORCID,Ntouyas Sotiris K.³^ORCID,Tariboon Jessada⁴^ORCID

Affiliation:

1. Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran

2. Department of Mathematics, University of Texas at San Antonio, San Antonio, TX 78249, USA

3. Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece

4. 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

Abstract

We aim to investigate the stability property for the certain linear and nonlinear fractional q-difference equations in the Ulam–Hyers and Ulam–Hyers–Rassias sense. To achieve this goal, we prove that three types of the linear q-difference equations of the q-Caputo-like type are Ulam–Hyers stable by using the quantum Laplace transform and quantum Mittag–Leffler function. Moreover, after proving the existence property for a nonlinear Cauchy q-difference initial value problem, we use the same quantum Laplace transform and the q-Gronwall inequality to show that it is generalized Ulam–Hyers–Rassias stable.

Funder

National Science, Research and Innovation Fund

Publisher

MDPI AG

Link

https://www.mdpi.com/2504-3110/8/8/443/pdf

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