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Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem
Joint Authors
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-01-08
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We firstly prove that β-times integrated α-resolvent operator function ((α,β)-ROF) satisfies a functional equation which extends that of β-times integrated semigroup and α-resolvent operator function.
Secondly, for the inhomogeneous α-Cauchy problem cDtαu(t)=Au(t)+f(t), t∈(0,T), u(0)=x0, u'(0)=x1, if A is the generator of an (α,β)-ROF, we give the relation between the function v(t)=Sα,β(t)x0+(g1*Sα,β)(t)x1+(gα-1*Sα,β*f)(t) and mild solution and classical solution of it.
Finally, for the problem cDtαv(t)=Av(t)+gβ+1(t)x, t>0, v(k)(0)=0, k=0,1,…,N-1, where A is a linear closed operator.
We show that A generates an exponentially bounded (α,β)-ROF on a Banach space X if and only if the problem has a unique exponentially bounded classical solution vx and Avx∈L loc 1(ℝ+,X).
Our results extend and generalize some related results in the literature.
American Psychological Association (APA)
Li, Ya-Ning& Sun, Hong-Rui. 2014. Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1013922
Modern Language Association (MLA)
Li, Ya-Ning& Sun, Hong-Rui. Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem. Abstract and Applied Analysis No. 2014 (2014), pp.1-9.
https://search.emarefa.net/detail/BIM-1013922
American Medical Association (AMA)
Li, Ya-Ning& Sun, Hong-Rui. Integrated Fractional Resolvent Operator Function and Fractional Abstract Cauchy Problem. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-9.
https://search.emarefa.net/detail/BIM-1013922
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013922