Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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ON THE STABILITY OF DIFFERENTIAL SYSTEMS INVOLVING 𝜓-HILFER FRACTIONAL DERIVATIVE

  • Limpanukorn, Norravich (Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi) ;
  • Ngiamsunthorn, Parinya Sa (Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi) ;
  • Songsanga, Danuruj (Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi) ;
  • Suechoei, Apassara (Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi)
  • Received : 2021.04.26
  • Accepted : 2022.03.20
  • Published : 2022.09.01
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Abstract

This paper deals with the stability of solutions to 𝜓-Hilfer fractional differential systems. We derive the fundamental solution for the system by using the generalized Laplace transform and the Mittag-Leffler function with two parameters. In addition, we obtained some necessary conditions on the stability of the solutions to linear fractional differential systems for homogeneous, non-homogeneous and non-autonomous cases. Numerical examples are also given to illustrate the behavior of solutions.

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Acknowledgement

The authors would like to thank referees for useful comments and feedback.

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