Fractional Cauchy Problems for Infinite Interval Case-II

Mohammed Al Horani, Mauro Fabrizio, Angelo Favini and Hiroki Tanabe
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Mohammed Al Horani: Department of Mathematics, The University of Jordan, Amman 11942, Jordan
Mauro Fabrizio: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
Angelo Favini: Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
Hiroki Tanabe: Takarazuka, Hirai Sanso 12-13, Osaka 665-0817, Japan

Mathematics, 2019, vol. 7, issue 12, 1-26

Abstract: We consider fractional abstract Cauchy problems on infinite intervals. A fractional abstract Cauchy problem for possibly degenerate equations in Banach spaces is considered. This form of degeneration may be strong and some convenient assumptions about the involved operators are required to handle the direct problem. Required conditions on spaces are also given, guaranteeing the existence and uniqueness of solutions. The fractional powers of the involved operator B X have been investigated in the space which consists of continuous functions u on [ 0 , ? ) without assuming u ( 0 ) = 0 . This enables us to refine some previous results and obtain the required abstract results when the operator B X is not necessarily densely defined.

Keywords: fractional derivative; abstract Cauchy problem; evolution equations; degenerate equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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