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Giusti, Andrea

On infinite order differential operators in fractional viscoelasticity. (English) Zbl 1439.74082

Fract. Calc. Appl. Anal. 20, No. 4, 854-867 (2017).
Summary: In this paper we discuss some general properties of viscoelastic models defined in terms of constitutive equations involving infinitely many derivatives (of integer and fractional order). In particular, we consider as a working example the recently developed Bessel models of linear viscoelasticity that, for short times, behave like fractional Maxwell bodies of order 1/2.

Cited in 21 Documents

MSC:

74D10 Nonlinear constitutive equations for materials with memory
35R11 Fractional partial differential equations
35Q74 PDEs in connection with mechanics of deformable solids
33C10 Bessel and Airy functions, cylinder functions, \({}_0F_1\)

Keywords:

infinite order differential operators; fractional calculus; Laplace transform; linear viscoelasticity; Bessel functions
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Full Text: DOI arXiv

References:

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