Mittag-Leffler-Hyers-Ulam stability for a first- and second-order nonlinear differential equations using Fourier transform. (English) Zbl 07899343
In this paper, the authors demonstrate the Hyers-Ulam and Hyers-Ulam-Rassias stability for first- and second-order nonlinear differential equations with initial conditions using the Fourier transform. They further extend the results to the Mittag-Leffler-Hyers-Ulam and Mittag-Leffler-Hyers-Ulam-Rassias stability.
Reviewer: Tunç Osman (Van)
MSC:
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
| 34B15 | Nonlinear boundary value problems for ordinary differential equations |
| 34D10 | Perturbations of ordinary differential equations |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
Keywords:
Fourier transform; Hyers-Ulam and Hyers-Ulam-Rassias stability; Mittag-Leffler-Hyers-Ulam and Mittag-Leffler-Hyers-Ulam-Rassias stability; nonlinear differential equationsReferences:
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