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

Bundit Unyong,Vediyappan Govindan,Chee Peng Lim,Grienggrai Rajchakit,Nallappan Gunasekaran,Anumanthappa Ganesh,R Vadivel,Arusamy Mohanapriya

doi:10.1186/s13662-020-03046-5

Abstract

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.

Highlights

In recent years, the area related to fractional differential and integral equations has received much attention from numerous mathematicians and specialists
An integral transform involves a trigonometric form of the Mittag-Leffler function to identify an analytic solution with respect to a differential equation of fractional order
In 2017, Wang et al [24] discussed the stability of fractional differential equation based on the right-sided Riemann–Liouville fractional derivatives with respect to a continuous function space

Summary

Introduction

The area related to fractional differential and integral equations has received much attention from numerous mathematicians and specialists. An integral transform (introduced by Fourier) involves a trigonometric form of the Mittag-Leffler function to identify an analytic solution with respect to a differential equation of fractional order. In 2017, Wang et al [24] discussed the stability of fractional differential equation based on the right-sided Riemann–Liouville fractional derivatives with respect to a continuous function space.

Results

Conclusion