On the fractional differential equations
type: Item
instance of: scholarly article
title: On the fractional differential equations
zbMATH Open document ID: 0757.34005
DOI: 10.1016/0096-3003(92)90024-U
published in: Applied Mathematics and Computation
publication date: 1992-09-27T00:00:00Z
review text: The author deals with the semilinear differential equation \(d^ \alpha x(t)/dt^ \alpha=f(t,x(t))\), \(t>0\), where \(\alpha\) is any positive real number. In [Kyungpook Math. J. 28, No. 2, 119-122 (1988; Zbl 0709.34011)] the author has proved the existence, uniqueness, and some properties of the solution of this equation when \(0<\alpha<1\). Here he mainly studies (besides the other properties) the continuation of the solution of this equation to the solution of the corresponding initial value problem when \([\alpha]=k\), \(k=1,2,3,\dots\;\). Applications of singular integro- differential equations are considered.
reviewed by: S. D. Bajpai
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 64330
zbMATH Keywords: semilinear differential equation
zbMATH Keywords: continuation
zbMATH Keywords: initial value problem
zbMATH Keywords: singular integro-differential equations
author: A. M. A. El-Sayed
MaRDI profile type: Publication
cites work: Q5333460
cites work: Functional analysis in modern applied mathematics
cites work: Q3491929
cites work: Q3265951
cites work: Q5567262
full work available at URL: 0096-3003(92)90024-u
OpenAlex ID: W1979359316
description: scientific article; zbMATH DE number 64330