Inverse Problems for Degenerate Fractional Integro-Differential Equations

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, 2020, vol. 8, issue 4, 1-11

Abstract: 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.

Keywords: fractional derivative; abstract Cauchy problem; evolution equation; inverse problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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