Le séminaire LCR accueille Zaid Odibat (Al-Balqa’ Applied University, Jordan).

Recently, the fractional derivative has drawn much attention due to its wide application in various fields of physics and engineering. Fractional derivatives provide an excellent instrument for the description of memory and hereditary properties of various materials and processes. The main reason for using the integer-order models was the absence of solution methods for fractional differential equations. The real objects of using fractional-order models are that we have more degrees of freedom in the model and that a “memory” is included in the model. Fractional-order systems have an unlimited memory.

In this presentation, we will, first, introduce the most used definitions of fractional derivatives and their properties then we will highlight some comments about differential equations of fractional order. Second, we will give an overview of the recent analytical-approximate methods that are used to provide approximate solutions for nonlinear differential equations of fractional order. Finally, we will introduce some important areas of applications, where the use of fractional order models is expected to be very suitable and useful. Theses areas included the control systems and the multi-scale processes.