A Theoretical Basis for the Application of Fractional Calculus to Viscoelasticity

Modeling of dynamic rotors with flexible bearings due to the use of viscoelastic materials

“…As stated before, the use of this model in describing the dynamic behavior of rotor systems with viscoelastic bearings is a novelty. According to Bagley and Torvik (1983), the unidimensional constitutive equation in terms of fractional derivatives is:…”

“…Generally, those works use the Kelvin-Voigt model, as proposed by Shabaneh and Jean (1999), where the viscoelastic material is put under the bearings. This model can not accurately represent the dynamic characteristics of most viscoelastic materials used in practice, particularly when a wide frequency band is considered (Pritz, 1996;Bagley and Torvik, 1983). It is stressed that this model is described by a differential equation of integer order.…”

Solvability of impulsive $$(n,n-p)$$ ( n , n - p ) boundary value problems for higher order fractional differential equations

“…On the other hand, higher order fractional differential equations have applications such as the fractional order elastic beam equations see [23], the fractional order viscoelastic material model see [24], the fractional viscoelastic model see [25][26][27] and so on. There has been no papers concerned with the solvability of boundary value problems for higher order impulsive fractional differential equations since it is difficult to convert an impulsive fractional differential equation to an equivalent integral equation.…”

Efficient solution of a vibration equation involving fractional derivatives

“…[1]). Several authors have been examining the possibility of using fractional derivatives in material modelling in the last two-three decades [2,3], and the field is of a growing interest A c c e p t e d m a n u s c r i p t nowadays [4][5][6][7][8][9]. Finite element formulations are also in development [9][10][11].…”