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Direct and Inverse Fractional Abstract Cauchy Problems
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Fractional Cauchy Problems for Infinite Interval Case-II

1
Department of Mathematics, The University of Jordan, Amman 11942, Jordan
2
Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy
3
Takarazuka, Hirai Sanso 12-13, Osaka 665-0817, Japan
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(12), 1165; https://doi.org/10.3390/math7121165
Received: 29 October 2019 / Revised: 17 November 2019 / Accepted: 19 November 2019 / Published: 2 December 2019
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. View Full-Text
Keywords: fractional derivative; abstract Cauchy problem; evolution equations; degenerate equations fractional derivative; abstract Cauchy problem; evolution equations; degenerate equations
MDPI and ACS Style

Al Horani, M.; Fabrizio, M.; Favini, A.; Tanabe, H. Fractional Cauchy Problems for Infinite Interval Case-II. Mathematics 2019, 7, 1165.

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