Analytical and numerical treatment of a fractional integro-differential equation of Volterra-type
type: Item
instance of: scholarly article
title: Analytical and numerical treatment of a fractional integro-differential equation of Volterra-type
zbMATH Open document ID: 0932.45012
DOI: 10.1016/S0895-7177(97)00090-3
author: H. G. Khajah
author: Lyubomir Boyadjiev
author: S. L. Kalla
published in: Mathematical and Computer Modelling
publication date: 2000-03-21T00:00:00Z
review text: The object of the paper is the study of the following fractional integro-differential equation \[ D^\alpha_ta(t)=\lambda\int^t_0sa(t-s)\exp(ics) ds,\quad t\in[0,1],\tag{1} \] where \(\lambda\) is a complex number, \(c\) is a real constant and \(\alpha\) is a positive real constant. The equations of the type (1) describe the behaviour of free electron laser. The derivative \(D^\alpha\) is defined as the so-called fractional derivative. The solution of (1) is obtained in terms of Kummer functions while the tau method is used in order to obtain approximations of solutions of (1) via the numerical estimates.
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 78A60
zbMATH DE Number: 1326449
zbMATH Keywords: Volterra-type
zbMATH Keywords: fractional integro-differential equation
zbMATH Keywords: electron laser
zbMATH Keywords: Kummer functions
zbMATH Keywords: tau method
Wikidata QID: Q115338617
reviewed by: Józef Banaś
MaRDI profile type: Publication
cites work: Q3864730
cites work: Q3141902
cites work: Q3141895
cites work: Q5820721
cites work: Q5544939
cites work: Q5563748
cites work: The Tau Method
cites work: Q4089262
cites work: Q3846497
full work available at URL: s0895-7177(97)00090-3
OpenAlex ID: W2085182367
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description: scientific article; zbMATH DE number 1326449