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

Advances in Difference Equations

article

Unyong, Bundit¹  Mohanapriya, Arusamy²  Ganesh, Anumanthappa³  Rajchakit, Grienggrai⁴  Govindan, Vediyappan⁵  Vadivel, R.¹  Gunasekaran, Nallappan⁶  Lim, Chee Peng⁷ 

[1] Department of Mathematics, Phuket Rajabhat University;Department of Mathematics, Adhiyamaan College of Engineering;Department of Mathematics, Government Arts and science College, Periyar University;Department of Mathematics, Faculty of Science, Maejo University;Department of Mathematics, Sri Vidya Mandir Arts & Science College;Department of Mathematical Sciences, Shibaura Institute of Technology;Institute for Intelligent Systems Research and Innovation, Deakin University

关键词: Fractional Fourier transform;    Fractional differential equation;    Hyers–Ulam stability;    Lizorkin space;    Mittag-Leffler function;    Riemann–Liouville derivative and integrals;   

DOI  :  10.1186/s13662-020-03046-5

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY