A study on fractional differential equations using the fractional Fourier transform

Advances in Difference Equations

article

Hammachukiattikul, Porpattama¹  Mohanapriya, Arusamy²  Ganesh, Anumanthappa³  Rajchakit, Grienggrai⁴  Govindan, Vediyappan⁵  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: Hyers–Ulam–Rassias stability;    Fourier transform;    Mittag-Leffler kernel;    Caputo–Fabrizio fractional differential equation;   

DOI  :  10.1186/s13662-020-03148-0

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY