Fractional calculus has been studied for over three centuries, and it has multifarious
applications in science and engineering. This review investigates its progress since the first …

A lot of automatic feedback control and learning tasks carried out on many dynamical
systems still fundamentally rely on a form of proportional–integral–derivative (PID) control …

Many real dynamic systems are better characterized using a non-integer order dynamic
model based on fractional calculus or, differentiation or integration of non-integer order …

In this paper we present a set of tuning rules for standard (integer-order) PID and fractional-
order PID controllers. Based on a first-order-plus-dead-time model of the process, the tuning …

In this article a new approach in solving time fractional partial differential equations
(TFPDEs) is introduced, that is, the ARA-residual power series method. The main idea of this …

This paper proposes a novel robust power system stabilizer (PSS), based on hybridization of
fractional order PID controller (PI λ D μ) and PSS for optimal stabilizer (FOPID-PSS) for the …

Stability as an extremely important property of dynamical systems can be investigated in
various domains (Bellman, 1953; Dorf and Bishop, 1990). The usual concept of the bounded …

This paper deals with a new method for analog implementation of the fractional-order
controller using an active element in form of the Operational Transconductance Amplifier …

In this paper, a fractional order (FO) PIλDμ controller is designed to take care of various
contradictory objective functions for an automatic voltage regulator (AVR) system. An …

The Riemann–Liouville fractional integral for repeated fractional integration is expanded in
block pulse functions to yield the block pulse operational matrices for the fractional order …