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Some probability densities and fundamental solutions of fractional evolution equations

Authors
Journal
Chaos Solitons & Fractals
0960-0779
Publisher
Elsevier
Publication Date
Volume
14
Issue
3
Identifiers
DOI: 10.1016/s0960-0779(01)00208-9
Disciplines
  • Mathematics

Abstract

Abstract In the present paper, if 0< α⩽1, we shall study the Cauchy problem in a Banach space E for fractional evolution equations of the form d αu dt α =Au(t)+B(t)u(t), where A is a closed linear operator defined on a dense set in E into E, which generates a semigroup and { B( t): t⩾0} is a family of a closed linear operators defined on a dense set in E into E. The existence and uniqueness of the solution of the considered Cauchy problem is studied for a wide class of the family of operators { B( t): t⩾0}. The solution is given in terms of some probability densities. An application is given for the theory of integro-partial differential equations of fractional orders.

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