Study of a Fractional Creep Problem with Multiple Delays in Terms of Boltzmann's Superposition Principle

Abstract

We study a class of nonlinear fractional differential equations with multiple delays, which is represented by the Voigt creep fractional model of viscoelasticity. We discuss two Voigt models, the first being linear and the second being nonlinear. The linear Voigt model give us the physical interpretation and is associated with important results since the creep function characterizes the viscoelastic behavior of stress and strain. For the nonlinear model of Voigt, our theoretical study and analysis provides existence and stability, where time delays are expressed in terms of Boltzmann's superposition principle. By means of the Banach contraction principle, we prove existence of a unique solution and investigate its continuous dependence upon the initial data as well as Ulam stability. The results are illustrated with an example.

arXiv commentThis is a preprint of a paper whose final and definite form is published Open Access in 'Fractal Fract.' at [https://doi.org/10.3390/fractalfract6080434]

References in corpus (5)

• Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives
• Approximate Controllability of Fractional Delay Dynamic Inclusions with Nonlocal Control Conditions
• Stability of a fractional HIV/AIDS model
• Global stability of a Caputo fractional SIRS model with general incidence rate
• An existence result for the fractional Kelvin-Voigt's model on time-dependent cracked domains