Dynamics of the fractional oscillator

Existence results for semilinear fractional differential equations via Kuratowski measure of noncompactness

“…In the last decades, fractional calculus and fractional differential equations have attracted much attention, we refer to [1,2,9,15,20,21,24,25], and references therein. It is found that many phenomena can be modeled with the help of fractional derivatives or integrals, such as fractional Brownian motion [5], anomalous diffusion [23,30], etc.…”

Microscopic Formulation of Fractional Theory of Viscoelasticity

“…However, this generalization does not require the dissipative elements, namely the dashpots to be explicitly considered, for the dissipation is intrinsic to the fractional oscillators [16][17][18][19].…”

“…However, as has been well known that a fractional oscillator behaves like a damped harmonic oscillator [15][16][17][18], the oscillations of the linear chain of fractional oscillators can be sustained only if it is driven by an external force. Hence a periodic force, taken to be sinusoidal without loss of generality, acting only on the first member of the chain is included.…”

Chaos in a fractional order logistic map

“…Fractional calculus applications to physics involve c 2013 Diogenes Co., Sofia pp. 511-519 , DOI: 10.2478/s13540-013-0033-8 viscoelastic systems and electro-magnetic waves [9], but also fractional order dynamical systems, fractional mechanics and fractional oscillators have been studied, [1,17]. Fractional order differential equations have appeared, for example, in fractional quantum mechanics as well as in fractional generalizations of the Einstein field equations and cosmology, [6,8].…”