Dear Walid,

First here is the bibliography of one of the specialists in this field. 

Also i suggest to you attach files and publication in topics.

Best regards

Article Kinetostatic modeling of 3-RRR compliant micro-motion stages...

Conference Paper Micro Position Control of a 3-RRR Compliant Mechanism

Article Tavazoei, M.S.: Notes on integral performance indices in fra...

Conference Paper On Fraction Order Modeling and Control of Dynamical Systems

Article Design a pre-compensator to guarantee the finiteness of inte...

Article Type Number Based Steady-State Error Analysis on Fractional ...

Hi Walid,

A Fractional Order Controller (FOC) typically uses the fractional-order derivative as “enhancement” in part of the mainstream control systems, such as fractional order sliding mode control, fractional order backstepping control, fractional order fuzzy control, and fractional order PID control. The following example shows how to design a simple fractional order sliding mode controller.

Consider a nonlinear control-affine system given by

x' = f(x) + Bu + d

where x is the state vector, f(x) is a smooth nonlinear function of its argument, B is the input matrix, u is the control vector, and d is the disturbance. A desired transformation

ς = λx

is introduced, where ς ∈ Rm×n and it is assumed that λB ≠ 0. Taking the time derivative of ς yield

ς' = λx'

and it easily follows that

ς' = λf(x) + λBu + λd.

The sliding manifold is chosen as

s = ς + Dας

where Dας is the fractional derivative term and 0 (1/2) απ.

On top of the valuable literature suggested by Prof. Lafifi and Prof. Khan, you are also advised to refer to Prof. YangQuan Chen's works in Fractional-Order Control Systems. Here is just one of the books.