Özbilge Kahveci, EbruDemir, Ali2023-06-162023-06-1620181303-5010https://doi.org/10.15672/HJMS.20164517213https://search.trdizin.gov.tr/yayin/detay/297434https://hdl.handle.net/20.500.14365/2340This 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 D(t)(alpha)u(x, t) = (k(x)u(x))(x) + F(x, t) 0 < alpha <= 1, with Robin boundary conditions u(0, t) = psi(0)(t), u(x)(1,t ) = gamma(u(1, t) - psi(1)(t)). By defining the input-output mappings Phi[.] : K -> C-1[0, T] and Psi[.] : K -> C[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 Phi[.] and Psi[.]. 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 Phi[.] : K -> C-1[0, T] and Psi[.] : K -> C[0, T] can be described explicitly.eninfo:eu-repo/semantics/openAccessInverse problemtime-fractional parabolic equationdistinguishabilityInverse ProblemDiffusionIdentificationApproximationArticle10.15672/HJMS.201645172132-s2.0-85073880288