Direct and Inverse Fractional Abstract Cauchy Problems

Mohammed AL Horani, Angelo Favini and Hiroki Tanabe
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Mohammed AL Horani: Department of Mathematics, The University of Jordan, Amman 11942, Jordan
Angelo Favini: Dipartimento di Matematica, Universita 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 11, 1-9

Abstract: 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 ? , p , p ? ( 0 , ? ] instead of the indices ? , ? . As a possible application of the abstract theorems, some examples of partial differential equations are given.

Keywords: fractional derivative; abstract Cauchy problem; C 0 ?semigroup; inverse problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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