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.
Highlights
A fractional order differential equation (FODE) is a generalized form of an integer order differential equation
This research direction hinges on the results reported by numerous researchers on complex systems of nonlocal elements, i.e., a local operator of ordinary derivative leads to a nonlocal fractional operator
We examine the existence of the Hyers–Ulam stability as well as Hyers– Ulam–Rassias stability of linear FODE
Summary
A fractional order differential equation (FODE) is a generalized form of an integer order differential equation. The FODE is useful in many areas, e.g., for the depiction of a physical model of various phenomena in pure and applied science (see [1,2,3,4] and the references therein). FODEs are considered as an alternative model to integer differential equation. Since many applications of the fractional derivatives and integrals of this Riemann–Liouville type have been demonstrated in numerous fields of science and technology. These include studies on controllability, stokes problem, thermoelasticity, vibration, and diffusion processes, bioengineering issues, and other complex phenomena (see [5,6,7])
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