Computational study on the dynamics of fractional order differential equations with applications

Kamal Shah, Muhammad Arfan, Aman Ullah, Qasem Al-Mdallal, Khursheed J. Ansari, Thabet Abdeljawad

Research output: Contribution to journalArticlepeer-review

64 Citations (Scopus)

Abstract

In this research work, the analysis of general fractional order system is investigated under Atangana, Baleanu and Caputo (ABC) fractional order derivative. Our study is related to three aspects including existence theory, stability and numerical analysis. For existence theory, we use Krasnoselskii and Banach contraction theorems. Further using nonlinear analysis, we develop some necessary results for Ulam Hyer's (UH) stability. The approximate solution is computed by using Adam's-Bashforth numerical technique. For justification, we provide three concert examples along with necessary numerical and graphical interpretations.

Original languageEnglish
Article number111955
JournalChaos, Solitons and Fractals
Volume157
DOIs
Publication statusPublished - Apr 2022

Keywords

  • Adam's-Bashforth method
  • Existence and uniqueness
  • Fractional general problems
  • Ulam Hyer's stability

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

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