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Title: Linear and nonlinear fractional voigt models
Author: Chidouh, Amar
Guezane-Lakoud, Assia
Bebbouchi, Rachid
Bouaricha, Amor
Torres, Delfim F.M.
Keywords: Creep phenomenon
Fixed point theorem
Fractional differential equation
Initial value problem
Mittag-Leffler function
Differential equations
Functional analysis
Ordinary differential equations
Existence results
Fractional generalization
Generalized Mittag Leffler function
Linear modeling
Volterra representation
Fixed point arithmetic
Issue Date: 2017
Publisher: Springer Verlag
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. © Springer International Publishing AG 2017.
Peer review: yes
DOI: 10.1007/978-3-319-45474-0_15
ISSN: 1876-1100
Appears in Collections:CIDMA - Artigos
SCG - Artigos

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