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Open AccessFeature PaperArticle

Direct and Inverse Fractional Abstract Cauchy Problems

1
Department of Mathematics, The University of Jordan, Amman 11942, Jordan
2
Dipartimento di Matematica, Universita 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(11), 1016; https://doi.org/10.3390/math7111016
Received: 7 September 2019 / Revised: 18 October 2019 / Accepted: 21 October 2019 / Published: 25 October 2019
We are concerned with a fractional abstract Cauchy problem for possibly degenerate equations in Banach spaces. This form of degeneration may be strong and some convenient assumptions about the involved operators are required to handle the direct problem. Moreover, we succeeded in handling related inverse problems, extending the treatment given by Alfredo Lorenzi. Some basic assumptions on the involved operators are also introduced allowing application of the real interpolation theory of Lions and Peetre. Our abstract approach improves previous results given by Favini–Yagi by using more general real interpolation spaces with indices θ , p, p ( 0 , ] instead of the indices θ , . As a possible application of the abstract theorems, some examples of partial differential equations are given. View Full-Text
Keywords: fractional derivative; abstract Cauchy problem; C0−semigroup; inverse problem fractional derivative; abstract Cauchy problem; C0−semigroup; inverse problem
MDPI and ACS Style

AL Horani, M.; Favini, A.; Tanabe, H. Direct and Inverse Fractional Abstract Cauchy Problems. Mathematics 2019, 7, 1016.

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