Mittag-Leffler–Hyers–Ulam stability of differential equation using Fourier transform

Abstract

This research paper aims to present the results on the Mittag-Leffler-Hyers-Ulam and Mittag-Leffler-Hyers-Ulam-Rassias stability of linear differential equations of first, second, and nth order by the Fourier transform method. Moreover, the stability constant of such equations is obtained. Some examples are given to illustrate the main results.

The Cădariu-Radu Method for Existence, Uniqueness and Gauss Hypergeometric Stability of Ω-Hilfer Fractional Differential Equations

“…we conclude that g(τ) satisfies the initial value problem Equation (1) if and only if g(τ) satisfies the integral Equation (8).…”

“…To see this note applying the fractional integral operator I S 1 ;Ω 0 + (.) on both sides of the fractional Equation (1) and using Theorem 2, we get (8).…”

“…The theory of fractional calculus (FC), developed rapidly and its application is done very widely nowadays. For more details, see [3][4][5][6][7][8].…”

Ulam type stability of second-order linear differential equations with constant coefficients having damping term by using the Aboodh transform

“…Murali et al [24] investigate the Hyers-Ulam stability of the linear differential equations by using the Fourier transform method (see also [24,25,33]). Mohanapriya et al [54] studied the Mittag-Leffler-Ulam stability for second order differential equations with constant coefficient by using the Fourier transform method. In 2014, Alqifiary and Jung [10] proved the Hyers-Ulam stability of linear differential equation (1.3).…”

Fractional Fourier transform and stability of fractional differential equation on Lizorkin space

“…At present, some remarkable results to the stability of fractional differential equation have been reported (see [28][29][30][31] and the references therein). In [32,33], the author studied the H-U stability of linear differential equation by using Fourier transform. To the best of our knowledge, there are no results on H-U stability of fractional differential equation by fractional Fourier transform (FRFT).…”