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Inverse Problems for Degenerate Fractional Integro-Differential Equations

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 2020, 8(4), 532; https://doi.org/10.3390/math8040532
Received: 19 February 2020 / Revised: 22 March 2020 / Accepted: 23 March 2020 / Published: 3 April 2020
(This article belongs to the Special Issue Direct and Inverse Problems for Fractional Differential Equations)
This paper deals with inverse problems related to degenerate fractional integro-differential equations in Banach spaces. We study existence, uniqueness and regularity of solutions to the problem, claiming to extend well known studies for the case of non-fractional equations. Our method is based on transforming the inverse problem to a direct problem and identifying the conditions under which this direct problem has a unique solution. The conditions under which the unique strict solution can be compared with the case of a mild solution, obtained in previous studies under quite restrictive requirements, are on the underlying functions. Applications from partial differential equations are given to illustrate our abstract results. View Full-Text
Keywords: fractional derivative; abstract Cauchy problem; evolution equation; inverse problem fractional derivative; abstract Cauchy problem; evolution equation; inverse problem
MDPI and ACS Style

Al Horani, M.; Fabrizio, M.; Favini, A.; Tanabe, H. Inverse Problems for Degenerate Fractional Integro-Differential Equations. Mathematics 2020, 8, 532.

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