Mittag–Leffler stability for a fractional Euler–Bernoulli problem

Nasser-eddine Tatar

Chaos, Solitons & Fractals, 2021, vol. 149, issue C

Abstract: We investigate the stability of an Euler–Bernoulli type problem of fractional order. By adding a fractional term of lower-order, namely of order half of the order of the leading fractional derivative, the problem will generalize the well-known telegraph equation. It is shown that this term is capable of stabilizing the system to rest in a Mittag–Leffler manner. Moreover, we consider a much weaker dissipative term consisting of a memory term in the form of a convolution known as viscoelastic term. It is proved that we can still obtain Mittag–Leffler stability under a smallness condition on the involved kernels. The results rely heavily on some established properties of fractional derivatives and some newly introduced functionals.

Keywords: Caputo fractional derivative; Mittag–Leffler stability; Multiplier technique (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:149:y:2021:i:c:s0960077921004318

DOI: 10.1016/j.chaos.2021.111077

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