This study aims to use the fractional Fourier transform for analyzing various types of Hyers–Ulam stability pertaining to the linear fractional order differential equation with Atangana and Baleanu fractional derivative. Specifically, we establish the Hyers–Ulam–Rassias stability results and examine their existence and uniqueness for solving nonlinear problems. Simulation examples are presented to validate the results.

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 use of Fourier transform has increased in the light of recent events in different application. Fourier transform is also seen as the easiest and an effective way among the other transformation. In line with this, the research deals with the Hyers-Ulam stability of second order differential equation using Fourier transform. The study aims at deriving a generalized Hyers-Ulam results for second order differential equations with constant co-efficient H ″ ( v ) + a H ′ ( v ) + b H ( v ) = r ( t ) with the help of Fourier Transform.

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In the current study, we conduct an investigation into the Hyers–Ulam stability of linear fractional differential equation using the Riemann–Liouville derivatives based on fractional Fourier transform. In addition, some new results on stability conditions with respect to delay differential equation of fractional order are obtained. We establish the Hyers–Ulam–Rassias stability results as well as examine their existence and uniqueness of solutions pertaining to nonlinear problems. We provide examples that indicate the usefulness of the results presented.