Well-posedness of the inverse problem of time fractional heat equation in the sense of the Atangana-Baleanu fractional approach

• Published in: Alexandria engineering journal Vol. 59; no. 4; pp. 2261 - 2268
• Main Authors: Djennadi, Smina, Shawagfeh, Nabil, Arqub, Omar Abu
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.08.2020; Elsevier
• Subjects: Atangana-Baleanu derivative; Eigenfunctions expansion method; Inverse problem; Robin boundary conditions; Volterra integral equation; Atangana-Baleanu derivative; Eigenfunctions expansion method; Volterra integral equation; Robin boundary conditions; Inverse problem
• ISSN: 1110-0168
• DOI: 10.1016/j.aej.2020.02.010

In the present work, an inverse problem for the heat equation in two dimensional space with Robin boundary condition that involving a new fractional derivative, namely, Atangana-Baleanu approach with non-local and non-singular kernel is considered. An explicit solution set {u(x,y,t),a(t)} of the given inverse problem is obtained by using the eigenfunctions expansion method and the integral overdetermination condition. Under some assumptions the existence, uniqueness of the suggested solution, and its continuous dependence on the data are proved.