Overview of Literature

Hereafter, a list of printed works, related to fractional calculus and its applications in modeling in controls, is presented with a brief overview1.

Fractional-order Systems and Controls: Fundamentals and Applications

Fractional-order Systems and Controls

by Concepción A. Monje, YangQuan Chen, Blas M. Vinagre, Dingyü Xue, and Vincente Feliu

This is one of the essential works that should definitely be in the collection of any scholar concerned with fractional-order calculus applications in modeling and control. This book is built up from the research efforts of the five authors and consists of 18 chapters, covering a wide range of problems related to fractional calculus, including modeling and analysis of fractional-order dynamical models, system identification, and control design with relevant MATLAB code for the FOTF toolbox, on which the core FOMCON functionality was based. Results from applying fractional-order controllers to real life applications are also provided.

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  • 1 Links to commercial websites, such as Amazon.com, may be provided in the list. The author is not directly affiliated with these websites and provides these links for the reader’s convenience.


  1. Amruta Mujumdar
    Posted June 6, 2013 at 12:58 | Permalink

    How to give initial condition to a fractional integrator like we give for integer order integrator?

    • Posted June 6, 2013 at 13:38 | Permalink

      The answer to this question depends on which definition of the fractional operator is considered. In FOMCON we currently assume zero initial conditions. Therefore, setting initial conditions for fractional-order operators is not yet implemented.

      • Emmanuel A. Gonzalez
        Posted September 3, 2013 at 14:36 | Permalink

        The issue on initial conditions is still dabatable because derivative initial condition is not necessarily the same as system (engineering) initial condition. Explanation regarding this can be found in Manuel Duarte Ortigueira’s papers:

        M. D. Ortigueira & F. J. Coito, “System initial conditions vs derivative initial conditions,” Computers and Mathematics with Applications, vol. 59, 2010, pp. 1782-1789.

        M. D. Ortigueira, “On the initial conditions in continuous-time fractional linear systems,” Signal Processing, vol. 83, 2003, pp. 2301-2309.

        From the papers, the author say that the Grunwald-Letnikov definition is most appropriate, but other researchers argue that Caputo is better.

  2. lifei
    Posted June 7, 2014 at 03:02 | Permalink

    where is the simulink model described “Figure 6.28:FOMCON simulink library”in you master degree paper?

  3. anitha
    Posted June 21, 2014 at 07:56 | Permalink

    I have seen the book sent by you as a reference for fractional PID..But its not been viewed completely..Please can you suggest a way so that i can view it completely

  4. saurabh
    Posted January 14, 2015 at 13:51 | Permalink

    May you please tell me any example of how to use function oustapid.m. For example I want the fractional order PID of Kp=1;Ki=2;lam=1.5;Kd=3;mu=1.8. what will be the command used in MATLAB to get Oustaloup approximation. I have tried “Gc = oustapid(1, 2, 1.5, 3, 1.8)” in MATLAB 2009 but it is not working.

    Posted February 13, 2015 at 07:55 | Permalink

    With reference in the book Fractional order systems and Controls, Design of fractional PD controllers is derived. with reference to fractional PD Controller design procedure, i tired to design Fractional PID controller to find the Kp,Ki,Kd,Lamda and Mu value. But it has more complex to find the those values using derivation and given condition.
    Is there any procedure to determine those values ? or
    Is the derivation of Fractional PID controller is available?
    Is there any some other techniques available ?
    if fpid_optim tools is used, then how can i Justify the those values?
    Is there any coding available?

  6. Vanchinathan
    Posted June 28, 2015 at 15:56 | Permalink

    Dear sir
    i’m doing research work in the area of Fractional order PID controller. i have two questions sir the firstone Kindly give design procedure for FOPID Controller and Give some sample m file program.
    second one How to design FOPID controller tunning methods by using optimization algorithms
    Pls reply me sir

  7. gowtham
    Posted February 25, 2017 at 14:42 | Permalink

    Respected Sir,

    I need some guidance of you which I request kindly.
    Sir, I would like to know about “fotf gui” where I need to find out lamda and mu values of a transfer function.
    ​Please guide me how to use this gui environment of fotf…

    Thanks & Regards.
    J Gowtham

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