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

Advances in Difference Equations

Nallappan Gunasekaran¹  Arusamy Mohanapriya²  Grienggrai Rajchakit³  Anumanthappa Ganesh⁴  Bundit Unyong⁵  R. Vadivel⁵  Vediyappan Govindan⁶  Chee Peng Lim⁷ 

[1] Department of Mathematical Sciences, Shibaura Institute of Technology, Omiya, 337-8570, Saitama, Japan;Department of Mathematics, Adhiyamaan College of Engineering, Hosur, Tamilnadu, India;Department of Mathematics, Faculty of Science, Maejo University, Sansai, 50290, Chiang Mai, Thailand;Department of Mathematics, Government Arts and science College, Periyar University, Hosur, Tamilnadu, India;Department of Mathematics, Phuket Rajabhat University, 83000, Phuket, Thailand;Department of Mathematics, Sri Vidya Mandir Arts & Science College, Katteri, Uthangarai, India;Institute for Intelligent Systems Research and Innovation, Deakin University, Waurn Ponds, 3216, VIC, Australia;

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

来源: Springer

【 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