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arXiv · 1606.06157

Linear and nonlinear fractional Voigt models

Amar Chidouh·Assia Guezane-Lakoud·Rachid Bebbouchi·Amor Bouaricha·Delfim F. M. Torres
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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.

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Amar Chidouh, Assia Guezane-Lakoud, Rachid Bebbouchi, Amor Bouaricha, Delfim F. M. Torres. 2016-06-12. Linear and nonlinear fractional Voigt models. https://doi.org/10.1007/978-3-319-45474-0_15

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