On a \(q\)-fractional variant of nonlinear Langevin equation of different orders
type: Item
instance of: scholarly article
title: On a \(q\)-fractional variant of nonlinear Langevin equation of different orders
zbMATH Open document ID: 1338.34011
DOI: 10.3103/S1068362314060041
author: Bashir Ahmad
author: Ahmed Alsaedi
author: Juan J. Nieto
author: Hana Al-Hutami
published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences
publication date: 2015-12-18T00:00:00Z
review text: For given numbers \(\beta,\gamma\in(0,1)\), the authors study a boundary value problem for the \(q\)-fractional nonlinear Langevin equation of different orders with \(q\)-fractional antiperiodic boundary conditions in the form \[ {}^c\!D^{\beta}_q({}^c\!D^\gamma_q+\lambda)x(t)= \rho f(t,x(t))+\delta I^\zeta_qg(t,x(t)), \;\;0\leq t\leq 1, \;\;0<q<1, \] \[ x(0)=-x(1),\;\;{}^c\!D^\gamma_qx(0)=-{}^c\!D^\gamma_qx(1), \] where \({}^c\!D^{\beta}_q\) and \({}^c\!D^\gamma_q\) denote the Caputo type fractional \(q\)-derivative, \(I^\zeta_{q,0}(\cdot)=I^\zeta_{q}(\cdot)\) denotes the Riemann-Liouville integral with \(0<\zeta<1\), \(f\), \(g\) are given continuous functions, \(\lambda\neq0\), and \(\rho\), \(\delta\) are real constants. Some existence results for solutions of the given problem are established by means of classical tools of fixed point theory. An illustrative example is also presented.
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6521985
zbMATH Keywords: Langevin equation
zbMATH Keywords: \(q\)-fractional
zbMATH Keywords: antiperiodic
zbMATH Keywords: existence
zbMATH Keywords: fixed point
Wikidata QID: Q60199315
reviewed by: Oleg Anashkin
MaRDI profile type: Publication
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full work available at URL: s1068362314060041
OpenAlex ID: W2473566468
description: scientific article; zbMATH DE number 6521985