1. bookVolumen 79 (2021): Edición 2 (December 2021)
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eISSN
1338-9750
Primera edición
12 Nov 2012
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3 veces al año
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Oscillation Behaviour of Solutions for a Class of a Discrete Nonlinear Fractional-Order Derivatives

Publicado en línea: 01 Jan 2022
Volumen & Edición: Volumen 79 (2021) - Edición 2 (December 2021)
Páginas: 101 - 118
Recibido: 22 May 2020
Detalles de la revista
License
Formato
Revista
eISSN
1338-9750
Primera edición
12 Nov 2012
Calendario de la edición
3 veces al año
Idiomas
Inglés
Abstract

Based on the generalized Riccati transformation technique and some inequality, we study some oscillation behaviour of solutions for a class of a discrete nonlinear fractional-order derivative equation Δ[γ()[α()+β()Δμu()]η]+ϕ()f[G()]=0,N0+1μ, \[\Delta [\gamma (\ell ){[\alpha (\ell ) + \beta (\ell ){\Delta ^\mu }u(\ell )]^\eta }] + \phi (\ell )f[G(\ell )] = 0,\ell \in {N_{{\ell _0} + 1 - \mu }},\] where 0>0,G()=j=01+μ(j1)(μ)u(j)\[{\ell _0} > 0,\quad G(\ell ) = \sum\limits_{j = {\ell _0}}^{\ell - 1 + \mu } {{{(\ell - j - 1)}^{( - \mu )}}u(j)} \] and Δμ is the Riemann-Liouville (R-L) difference operator of the derivative of order μ, 0 < μ ≤ 1 and η is a quotient of odd positive integers. Illustrative examples are given to show the validity of the theoretical results.

Keywords

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