Abstarct: The concepts of non-integer derivative and integral are the foundation of the fractional calculus. Non-integer derivative has become nowadays a precious tool, currently used in the study of the behavior of real systems in diverse fields of science and engineering. Starting from the sixties, the research in this domain of interest has progressively put to light important concepts associated with formulations using non-integer order derivative. Indeed, non-integer order derivative revealed to be a more adequate tool for the understanding of interesting properties shown by various types of physical phenomena, that is, fractality, recursivity, diffusion and/or relaxation phenomena.