Stability analysis of fractional differential equations with unknown parameters

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Köksal M. E.

NONLINEAR ANALYSIS-MODELLING AND CONTROL, vol.24, no.2, pp.224-240, 2019 (SCI-Expanded) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 2
  • Publication Date: 2019
  • Doi Number: 10.15388/na.2019.2.5
  • Journal Name: NONLINEAR ANALYSIS-MODELLING AND CONTROL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.224-240
  • Keywords: stability, fractional differential equations, fractional derivative, unknown parameters, parametric analysis, SYSTEMS, TRANSFORM
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. Using the graphical based D-decomposition method, the parametric stability analysis of FDEs is investigated without complicated mathematical analysis. To achieve this, stability boundaries are obtained firstly by a conformal mapping from 8-plane to parameter space composed by unknown parameters of FDEs, and then the stability region set depending on the unknown parameters is found. The applicability of the presented method is shown considering some benchmark equations, which are often used to verify the results of a new method. Simulation examples show that the method is simple and give reliable stability results.