Computational study on the dynamics of fractional order differential equations with applications. (April 2022)

• Record Type: Journal Article
• Authors: Shah, Kamal; Arfan, Muhammad; Ullah, Aman; Al-Mdallal, Qasem; Ansari, Khursheed J.; Abdeljawad, Thabet
• Is Part Of: Chaos, solitons and fractals. Volume 157(2022)
• Publication Date: 2022-04
• Subjects: Fractional general problems -- Adam's-Bashforth method -- Existence and uniqueness -- Ulam Hyer's stability; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.111955
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: We study a general dynamical system. We establish the existence theory. We develop a numerical scheme based on Adam Bashforth method. Numerical interpretation along with stability have been done. 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.