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

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. (c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

This research work investigates the analysis of a general fractional order system under Atangana, Baleanu, and Caputo (ABC) fractional order derivative. The study focuses on existence theory, stability, and numerical analysis. The Krasnoselskii and Banach contraction theorems are used for the existence theory, and necessary results for Ulam Hyer's (UH) stability are developed using nonlinear analysis. The approximate solution is computed using the Adam's-Bashforth numerical technique, and three concrete examples with numerical and graphical interpretations are provided for validation.