NDLI: Hyers-Ulam-Mittag-Leffler stability of fractional differential equations with two caputo derivative using fractional fourier transform

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Hyers-Ulam-Mittag-Leffler stability of fractional differential equations with two caputo derivative using fractional fourier transform

Content Provider	Directory of Open Access Journals (DOAJ)
Author	Vediyappan Govindan Shyam Sundar Santra Swaminathan Deepa Dumitru Baleanu Osama Moaaz Anumanthappa Ganesh Rifaqat Ali
Abstract	In this paper, we discuss standard approaches to the Hyers-Ulam Mittag Leffler problem of fractional derivatives and nonlinear fractional integrals (simply called nonlinear fractional differential equation), namely two Caputo fractional derivatives using a fractional Fourier transform. We prove the basic properties of derivatives including the rules for their properties and the conditions for the equivalence of various definitions. Further, we give a brief basic Hyers-Ulam Mittag Leffler problem method for the solving of linear fractional differential equations using fractional Fourier transform and mention the limits of their usability. In particular, we formulate the theorem describing the structure of the Hyers-Ulam Mittag Leffler problem for linear two-term equations. In particular, we derive the two Caputo fractional derivative step response functions of those generalized systems. Finally, we consider some physical examples, in the particular fractional differential equation and the fractional Fourier transform.
Related Links	https://www.aimspress.com/article/doi/10.3934/math.2022103?viewType=HTML
e-ISSN	24736988
DOI	10.3934/math.2022103
Journal	AIMS Mathematics
Issue Number	2
Volume Number	7
Language	English
Publisher	AIMS Press
Publisher Date	2022-01-01
Publisher Place	United States
Access Restriction	Open
Subject Keyword	Mathematics Fractional Fourier Transform Fractional Differential Equation Hyers-ulam-mittag-leffler Stability Mittag-leffler Function Caputo Derivative
Content Type	Text
Resource Type	Article

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