A new fractional viscoelastic model for an infinitely thermoelastic body with a spherical cavity including Caputo-Fabrizio operator without singular kernel

Almost sure stability of Caputo Fractional-order Markovian switching nonlinear systems

“…In many practical problems, due to the non-locality and memory of fractional operator, it can more accurately describe the physical process and behavior changes. Fractional derivative model is widely used in multi-agent systems [1], viscoelastic systems [2,3], permanent magnet synchronous motors [4,5], and so on.…”

Wave process in viscoelastic media using fractional derivatives with non singular kernels

“…In the field of biology, medicine, petroleum, chemical, and civil engineering, viscoelastic materials, such as rubbers, elastomers, resins, concrete, and skeletons, are common. They have become one of the potential options for novel multifunctional materials due to their excellent intrinsic rheological properties [2][3][4].…”

“…Some of the first works to deal with interesting aspects of the application of fractional calculus in viscoelasticity are considered in [34][35][36][37] A wide variety of linear and nonlinear constitutive models are proposed to define the viscoelastic deformation process of viscoelastic materials in order to explore their mechanical behavior. The models most used by Young Operator include the Kelvin-Voigt, Maxwell derivative relation, and the standard linear solid model to describe viscoelastic objects such as beams, plates, and shells, considering the Poisson ratio as continuous for viscoelastic materials [2,11,12].…”

“…However, the integer-order constitutive stress-strain coupling for conventional viscoelasticity has been questioned because the expected early stages of creep and relaxation do not match the experimental evidence [2,13]. This is mainly due to the fact that the integer-order differential equations of traditional viscoelastic models may fail in some situations, such as stress relaxation in polymer foams [2,14] and ultra-slow relaxation in polymer thin films [2,15]. Fractional order calculus provides a suitable alternative, in order to replace the relation of the classical viscoelastic foundational model, by the theoretical modification of mechanical deformation [2,16,17].…”

“…This is mainly due to the fact that the integer-order differential equations of traditional viscoelastic models may fail in some situations, such as stress relaxation in polymer foams [2,14] and ultra-slow relaxation in polymer thin films [2,15]. Fractional order calculus provides a suitable alternative, in order to replace the relation of the classical viscoelastic foundational model, by the theoretical modification of mechanical deformation [2,16,17]. The fractional viscoelastic model uses fractional order derivatives to correlate stress fields with areas of deformation in viscoelastic materials.…”