Ozbilge, E.Demir, A.Kanca, F.Özbilge, E.2023-10-192023-10-19201631935-0090https://doi.org/10.18576/amis/100129https://hdl.handle.net/20.500.12469/4845This article deals with the mathematical analysis of the inverse problem of identifying the distinguishability of input-output mappings in the linear time fractional inhomogeneous parabolic equation Dt ? u(x, t)=(k(x)ux)x+r(t)F(x, t) 0 < ? ? 1, with Dirichlet boundary conditions u(0, t) = ?0(t), u(1, t) = ?1(t). By defining the input-output mappings ?[·]: K ?C1[0,T ] and ?[·]: K ? C1[0,T] the inverse problem is reduced to the problem of their invertibility. Hence, the main purpose of this study is to investigate the distinguishability of the input-output mappings ?[·] and ?[·]. Moreover, the measured output data f (t) and h(t) can be determined analytically by a series representation, which implies that the input-output mappings ? [·] :K ? C1[0,T] and ?[·] :K ? C1[0,T] can be described explicitly. © 2016 NSP Natural Sciences Publishing Cor.eninfo:eu-repo/semantics/closedAccessDistinguishabilityFractional parabolic equationSource functionArticle28328911010.18576/amis/1001292-s2.0-84959175835N/AQ3