Mittag-Leffler-Hyers-Ulam stability for a first- and second-order nonlinear differential equations using Fourier transform

Abstract

In this article, we apply the Fourier transform to prove the Hyers-Ulam and Hyers-Ulam-Rassias stability for the first- and second-order nonlinear differential equations with initial conditions. Additionally, we extend the results to investigate the Mittag-Leffler-Hyers-Ulam and Mittag-Leffler-Hyers-Ulam-Rassias stability of these differential equations using the proposed method.

Keywords

• fourier transform
• hyers-ulam and hyers-ulam-rassias stability
• mittag-leffler-hyers-ulam and mittag-leffler-hyers-ulam-rassias stability
• nonlinear differential equations
• 34k20
• 26d10
• 39b82
• 34a40
• 39a30