Bifurcation analysis of dynamical systems with fractional order differential equations via the modified Riemann-Liouville derivative

J. M.  AL-Rmali; R. A.  Shahein

doi:10.24297/jam.v22i.9535

Authors

J. M. AL-Rmali Department of Mathematics, Faculty of sciences of Al-Jouf University, Saudi Arabia.
R. A. Shahein Department of Mathematics, College of Science, Taibah University, Saudi Arabia.

DOI:

https://doi.org/10.24297/jam.v22i.9535

Keywords:

Mittage-Leffler function, Fractional differential equations, Modified Riemann-Liouville derivative, Dynamical systems

Abstract

In this manuscript, the solutions of linear dynamical systems with fractional differential equations via the
modified Riemann-Liouville derivative is derived. By using Jumarie type of derivative (JRL), we stated and proved
the Existence and uniqueness theorems of the dynamical systems with fractional order equations. Also a novel stability analysis of fractional dynamical systems by Jumarie type derivative is established and some important stability conditions are determined. The achieved results have various applications in mathematics, plasma physics and almost all branches of physics that have non-conservative forces. Finally, we investigated interesting application of nonlinear space-time fractional Korteweg-de Vries (STFKdV) equation in Saturn F-ring’s region. Moreover, our investigation could be basic interest to explain and interpret the effects of fractional and modification parameters on STFKdV equation. This is novel study on this model by dynamical system (DS) to describe the behavior of nonlinear waves without solve this system.

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