2013/04/02 by Mohammed-Salah Abdelouahab, Abdelouahab, Mohammed-Salah, Nasr-Eddine Hamri +1
Engineering · Mathematics · #Advanced Control Systems Design #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Fractional Differential Equations Solutions
paper · pdf · doi:10.48550/arxiv.1304.0616
openalex publication_date 2013/04/02 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28
Contrary to integer order derivative, the fractional-order derivative of a\nnon-constant periodic function is not a periodic function with the same period,\nas a consequence of this property the time-invariant fractional order system\ndoes not have any non-constant periodic solution unless the lower terminal of\nthe derivative is plus or minus infinite, which is not practical. This property\nlimits the applicability areas of fractional derivatives and makes it\nunfavorable, for a wide range of periodic real phenomena. Therefore enlarging\nthe applicability of fractional system to such real area is an important\nresearch topic. In this paper we give a solution for the above problem by\nimposing a simple modification on the Gr "unwald-Letnikov definition of\nfractional derivative, this modification consists of fixing the memory length\nand varying the lower terminal of the derivative. It is shown that the new\nproposed definition of fractional derivative preserves the periodicity.\n