Asymptotic Behavior for Fractional Systems with Lower-Order Fractional Derivatives

Mohammed D. Kassim*, Nasser Eddine Tatar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

The asymptotic behavior, the decay and the boundedness of solutions are discussed for the system of fractional differential equations including two types of fractional derivatives the Caputo fractional derivative (CFD) and the Riemann-Liouville fractional derivative (RLFD). Reasonable sufficient conditions are determined ensuring that solutions for the system with nonlinear right hand sides approach a power type function, power type decay and boundedness as time goes to infinity. Our approach is based on appropriate desingularization techniques and generalized the inequality of the Gronwall-Bellman. Convenient assessments and lemmas such as a fractional version of L’Hopital’s rule are used.

Original languageEnglish
Pages (from-to)145-166
Number of pages22
JournalProgress in Fractional Differentiation and Applications
Volume9
Issue number1
DOIs
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2023 NSP Natural Sciences Publishing Cor.

Keywords

  • Asymptotic behavior
  • Riemann-Liouville and Caputo fractional derivatives
  • boundedness
  • desingularization technique
  • fractional differential equation
  • power type decay
  • weighted space

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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