In this paper, we incorporate fuzzy reasoning in fractional-order PD controllers. The resulting fuzzy fractional PD controller is investigated in terms of its digital implementation and robustness. The combined features of both algorithms will result in a better control system performance. Also, the effectiveness and robustness of the new methodology is illustrated through an application exampl...

Abstract Viscoelastic damping material has been widely used in engineering machinery to absorb vibration and noise. Dynamic behavior of the viscoelastic is mainly affected by temperature frequency. Classical dynamic equations have complex structures with multiple ambiguous parameters. So a novel variable-order fractional constitutive model (VOFC) established based on operator. Then are derived ...

Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the same idea for fractional variational problems. We consider a minimization problem with a Lagrangian that depends only on the left Riemann–Liouville fractional ...