Necessary and sufficient stability instability conditions are reviewed extended for multi-term homogeneous linear fractional differential equations with Caputo derivatives constant coefficients. A comprehensive review of the state art regarding analysis two-term three-term fractional-order is provided, which then to case four-term equations. The properties characterized respect coefficients equ...

This study presents a collocation approach for the numerical integration of multi-order fractional differential equations with initial conditions in Caputo sense. The problem was transformed from its integral form into system linear algebraic equations. Using matrix inversion, are solved and their solutions substituted approximate equation to give results. effectiveness precision method were il...

In this paper, we directly derive a new discrete state space expression of the fractional order chaotic system based on the fractional order Grnwald-Letnikow(G-L) definition and design a variable structure controller with a new faster reachinglaw. The new reaching-law has the advantages of weakening the high frequency shake. Firstly, the condition of the discrete sliding mode surface is demonst...