Inverse Problems for Degenerate Fractional Integro-Differential Equations

Mathematics

Mohammed Al Horani¹  Mauro Fabrizio²  Angelo Favini²  Hiroki Tanabe³ 

[1] Department of Mathematics, The University of Jordan, Amman 11942, Jordan;Dipartimento di Matematica, Università di Bologna, Piazza di Porta S. Donato 5, 40126 Bologna, Italy;Takarazuka, Hirai Sanso 12-13, Osaka 665-0817, Japan;

关键词: fractional derivative;    abstract Cauchy problem;    evolution equation;    inverse problem;   

DOI  :  10.3390/math8040532

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown