Positive Solutions for the Initial Value Problems of Fractional Evolution Equation
Joint Authors
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-11-04
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
This paper discusses the existence of positive solutions for the initial value problem of fractional evolution equation with noncompact semigroup Dqu(t)+Au(t)=f(t,u(t)), t≥0; u(0)=u0 in a Banach space X, where Dq denotes the Caputo fractional derivative of order q∈(0,1), A:D(A)⊂X→X is a closed linear operator, -A generates an equicontinuous C0 semigroup, and f:[0,∞)×X→X is continuous.
In the case where f satisfies a weaker measure of noncompactness condition and a weaker boundedness condition, the existence results of positive and saturated mild solutions are obtained.
Particularly, an existence result without using measure of noncompactness condition is presented in ordered and weakly sequentially complete Banach spaces.
These results are very convenient for application.
As an example, we study the partial differential equation of parabolic type of fractional order.
American Psychological Association (APA)
Liang, Yue& Ma, Yu& Gao, Xiaoyan. 2013. Positive Solutions for the Initial Value Problems of Fractional Evolution Equation. Journal of Function Spaces،Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-1006254
Modern Language Association (MLA)
Liang, Yue…[et al.]. Positive Solutions for the Initial Value Problems of Fractional Evolution Equation. Journal of Function Spaces No. 2013 (2013), pp.1-8.
https://search.emarefa.net/detail/BIM-1006254
American Medical Association (AMA)
Liang, Yue& Ma, Yu& Gao, Xiaoyan. Positive Solutions for the Initial Value Problems of Fractional Evolution Equation. Journal of Function Spaces. 2013. Vol. 2013, no. 2013, pp.1-8.
https://search.emarefa.net/detail/BIM-1006254
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1006254