A study on fractional differential equations using the fractional Fourier transform

Abstract

Abstract 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.

Keywords

• Hyers–Ulam–Rassias stability
• Fourier transform
• Mittag-Leffler kernel
• Caputo–Fabrizio fractional differential equation