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

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...

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Bibliographic Details
Published in:Advances in Difference Equations Vol. 2020; no. 1; pp. 1 - 23
Main Authors: Unyong, Bundit, Mohanapriya, Arusamy, Ganesh, Anumanthappa, Rajchakit, Grienggrai, Govindan, Vediyappan, Vadivel, R., Gunasekaran, Nallappan, Lim, Chee Peng
Format: Journal Article
Language:English
Published: Cham Springer Science and Business Media LLC 16.10.2020
Springer International Publishing
SpringerOpen
Subjects:
Analysis
Difference and Functional Equations
Fractional differential equation
Fractional Fourier transform
Functional Analysis
Hyers–Ulam stability
Lizorkin space
Mathematics
Mathematics and Statistics
Mittag-Leffler function
Ordinary Differential Equations
Partial Differential Equations
QA1-939
Riemann–Liouville derivative and integrals
Fractional differential equation
Lizorkin space
Hyers–Ulam stability
Mittag-Leffler function
Riemann–Liouville derivative and integrals
Fractional Fourier transform
ISSN:1687-1847, 1687-1847
Online Access:Get full text
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Summary: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.
ISSN:1687-1847
1687-1847
DOI:10.1186/s13662-020-03046-5