Numerical analysis for compact difference scheme of fractional viscoelastic beam vibration models

Li, Qing; Chen, Huanzhen

doi:10.1016/j.amc.2022.127146

Cited by 4 publications

(1 citation statement)

References 26 publications

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“…In recent years, fractional calculus has attracted the attention of many researchers [1][2][3][4][5][6][7]. Such a research axis is of great importance in many fields, especially when dealing with memory or hereditary properties, such as in viscoelastic phenomena: for example, stressstrain in polymeric materials [8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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

Chidouh¹,

Atmania

Torres

2022

Fractal Fract

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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.

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