On a new structure of multi-term Hilfer fractional impulsive neutral Levin-Nohel integrodifferential system with variable time delay

Thabet Abdeljawad, Sabri T.M. Thabet, Imed Kedim, Miguel Vivas-Cortez*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The Levin-Nohel equations play key roles in the interpretation of real phenomena and have interesting applications in engineering and science areas, such as mathematical physics, mathematical biology, image processing, and numerical analyses. This article investigates a new structure for the delay neutral Levin-Nohel integrodifferential (NLNID) system via a Hilfer fractional derivative and is supplemented by initial and instantaneous impulse conditions. A fractional integral equation corresponding to the proposed system is derived and used to prove the existence and uniqueness of the solution with the help of the Banach contraction principle. Additionally, the Ulam-Hyers-MittagLeffler (UHML) stability is studied by utilizing the generalized Gronwall’s inequality and nonlinear analysis issues. As a consequence, the Ulam-Hyers (UH) stability and generalized UH are also deduced. Furthermore, the Riemann-Liouville (R.L.) and Caputo fractional versions of the proposed system are discussed. Finally, numerical applications supported with tables and graphics are provided to test the exactitude of the findings.

Original languageEnglish
Pages (from-to)7372-7395
Number of pages24
JournalAIMS Mathematics
Volume9
Issue number3
DOIs
Publication statusPublished - 2024
Externally publishedYes

Keywords

  • generalized Gronwall’s inequality
  • Hilfer fractional derivatives
  • impulsive condition
  • Leivn-Nohel equation
  • Ulam-Hyers-Mittag-Leffler stability

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