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

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...

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Published inAIMS mathematics Vol. 7; no. 2; pp. 1791 - 1810
Main Authors Ganesh, Anumanthappa, Deepa, Swaminathan, Baleanu, Dumitru, Santra, Shyam Sundar, Moaaz, Osama, Govindan, Vediyappan, Ali, Rifaqat
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2022
Subjects
caputo derivative
fractional differential equation
fractional fourier transform
hyers-ulam-mittag-leffler stability
mittag-leffler function
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ISSN2473-6988
2473-6988
DOI10.3934/math.2022103

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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.
AbstractList 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.
Author Moaaz, Osama
Govindan, Vediyappan
Ali, Rifaqat
Baleanu, Dumitru
Santra, Shyam Sundar
Ganesh, Anumanthappa
Deepa, Swaminathan
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CorporateAuthor Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Çankaya University Ankara, 06790 Etimesgut, Turkey
Department of Mathematics, Government Arts and Science College, Hosur, 635 110, Tamilnadu, India
Department of Mathematics, College of Science and Arts, Muhayil, King Khalid University, Abha 9004, Saudi Arabia
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
Department of Mathematics, Adhiyamaan college of engineering, Hosur, 635 109, Tamilnadu, India
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, China
Department of Mathematics, JIS College of Engineering, Kalyani, West Bengal-741 235, India
Department of Mathematics, Phuket Rajabhat University, 83000, Thailand
Instiute of Space Sciences, Magurele-Bucharest, 077125 Magurele, Romania
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StartPage 1791
SubjectTerms caputo derivative
fractional differential equation
fractional fourier transform
hyers-ulam-mittag-leffler stability
mittag-leffler function
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Title Hyers-Ulam-Mittag-Leffler stability of fractional differential equations with two caputo derivative using fractional fourier transform
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