An Introduction to Fractional Control

On simplified forms of the fractional-order backward difference and related fractional-order linear discrete-time system description

“…The mostly considered description of the linear discrete-time FO system (FOS) is as follows [1,11,15]…”

“…Now it is assumed that the system (26) and their approximations (31) and (32) are asymptotically stable. Moreover it is assumed that the system is subjected to an input signal preserving the steady-state of the solution [13][14][15]. The last statement means that the one-sided Z-transform of the input signal u k can be splitted into a form…”

Fractional Definite Integral

“…Fractional Calculus has evolved considerably during the last 30 years and has become popular in many scientific and technical areas [1][2][3][4]. The progress in applications vis-a-vis theoretical developments motivated the re-evaluation of past formulations.…”

A fractional perspective to the bond graph modelling of world economies

“…This idea leads to the area usually known as 'Fractional Calculus' (FC) and represents the generalization of the operations of integration and differentiation up to real or complex orders [34,46,49,52,55,57]. During the last decades researchers verified that fractional models capture memory effects of natural and artificial phenomena, while classical integer models reveal limitations when describing those properties [6,29,44,65,71]. This state of affairs has motivated an intensive research towards new areas of application of the novel concepts, and we verify a sustained growth in the number of publications involving this mathematical tool [42,43].…”