Introduction

Gorenflo, Rudolf; Kilbas, Anatoly A.; Mainardi, Francesco; Rogosin, Sergei

doi:10.1007/978-3-662-43930-2_1

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Definitions and Propositions3

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Cited by 2 publications

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“…Definition 1. (Gorenflo et al, 2014;Podlubny, 1999) The Riemann-Liouville fractional integral of order γ > 0 is given by…”

Section: Definitions and Propositionsmentioning

confidence: 99%

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Mittag-Leffler stability for a Timoshenko problem

Tatar¹

2021

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A Timoshenko system of a fractional order between zero and one is investigated here. Using a fractional version of resolvents, we establish an existence and uniqueness theorem in an appropriate space. Moreover, it is proved that lower order fractional terms (in the rotation component) are capable of stabilizing the system in a Mittag-Leffler fashion. Therefore, they deserve to be called damping terms. This is shown through the introduction of some new functionals and some fractional inequalities, and the establishment of some properties, involving fractional derivatives. In the case of different wave speeds of propagation we obtain convergence to zero.

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“…Definition 1. (Gorenflo et al, 2014;Podlubny, 1999) The Riemann-Liouville fractional integral of order γ > 0 is given by…”

Section: Definitions and Propositionsmentioning

confidence: 99%

“…Definition 2. (Gorenflo et al, 2014;Podlubny, 1999) The fractional derivative of order γ in the sense of Caputo is given by…”

Section: Definitions and Propositionsmentioning

confidence: 99%

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Mittag-Leffler stability for a Timoshenko problem

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2021

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Undetermined Coefficients Method for Sequential Fractional Differential Equations

Erman¹

2023

Kocaeli Journal of Science and Engineering

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Undetermined coefficients method is presented for nonhomogeneous sequential fractional differential equations involving Caputo fractional derivative of order n\alpha where n-1 n\alpha\le\ n and n\in\mathbb{N}. By employing presented method, a particular solution of the considered equation is obtained. Some details about the estimation of the particular solution required to apply this method are explained. It is shown that this method is particularly effective for nonhomegenous fractional differential equations when the fractional differential equations involve some specific right-hand side functions.

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Introduction

Cited by 2 publications

References 222 publications

Mittag-Leffler stability for a Timoshenko problem

Mittag-Leffler stability for a Timoshenko problem

Undetermined Coefficients Method for Sequential Fractional Differential Equations

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