Linear and Nonlinear Fractional Voigt Models

Abstract

We consider fractional generalizations of the ordinary differential equation that governs the creep phenomenon. Precisely, two Caputo fractional Voigt models are considered: a rheological linear model and a nonlinear one. In the linear case, an explicit Volterra representation of the solution is found, involving the generalized Mittag-Leffler function in the kernel. For the nonlinear fractional Voigt model, an existence result is obtained through a fixed point theorem. A nonlinear example, illustrating the obtained existence result, is given.

A survey on fuzzy fractional differential and optimal control nonlocal evolution equations

“…They derived an effective spectral tau method under uncertainty by applying these functions to solve two important fractional dynamical models via the fuzzy Caputo-type fractional derivative. They proposed a new model based on fractional calculus to deal with the Kelvin-Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters (for Caputo fractional Voigt models see [95]). Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings.…”

Almost periodic fractional fuzzy dynamic equations on timescales: A survey

“…They derived an effective spectral tau method under uncertainty by applying these functions to solve two important fractional dynamical models by the fuzzy Caputo-type fractional derivative. They proposed a new model based on fractional calculus to deal with the Kelvin-Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters (for Caputo fractional Voigt models, see [127]). Numerical simulations are carried out, and the analysis of the results highlights the significant features of the new technique compared with the previous findings.…”

Existence Results for a Multipoint Fractional Boundary Value Problem in the Fractional Derivative Banach Space

“…A fractional derivative is a generalization of the ordinary one. Despite the emergence of several definitions of fractional derivative, the content is one that depends entirely on Volterra integral equations and their kernel, which facilitates the description of each phenomenon as a temporal lag, such as rheological phenomena [8][9][10].…”