Quantum Laplace Transforms for the Ulam–Hyers Stability of Certain q-Difference Equations of the Caputo-like Type
| dc.contributor.author | Etemad, Sina | |
| dc.contributor.author | Stamova, Ivanka | |
| dc.contributor.author | Ntouyas, Sotiris K. | |
| dc.contributor.author | Tariboon, Jessada | |
| dc.date.accessioned | 2024-08-28T13:59:54Z | |
| dc.date.available | 2024-08-28T13:59:54Z | |
| dc.date.issued | 2024-07-28 | |
| dc.date.updated | 2024-08-28T13:59:54Z | |
| dc.description.abstract | We aim to investigate the stability property for the certain linear and nonlinear fractional <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="monospace">q</mi></semantics></math></inline-formula>-difference equations in the Ulam–Hyers and Ulam–Hyers–Rassias sense. To achieve this goal, we prove that three types of the linear <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="monospace">q</mi></semantics></math></inline-formula>-difference equations of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="monospace">q</mi></semantics></math></inline-formula>-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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="monospace">q</mi></semantics></math></inline-formula>-difference initial value problem, we use the same quantum Laplace transform and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="monospace">q</mi></semantics></math></inline-formula>-Gronwall inequality to show that it is generalized Ulam–Hyers–Rassias stable. | |
| dc.identifier | doi: 10.3390/fractalfract8080443 | |
| dc.identifier.citation | Fractal and Fractional 8 (8): 443 (2024) | |
| dc.identifier.uri | https://hdl.handle.net/20.500.12588/6609 | |
| dc.title | Quantum Laplace Transforms for the Ulam–Hyers Stability of Certain q-Difference Equations of the Caputo-like Type |