This 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 α u(x, t)=(k(x)ux)x+r(t)F(x, t) 0 < α ≤ 1, with Dirichlet boundary conditions u(0, t) = Ψ0(t), u(1, t) = Ψ1(t). By defining the input-output mappings Φ[·]: K →C1[0,T ] and Ψ[·]: 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 Φ[·] and Ψ[·]. 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 Φ [·] :K → C1[0,T] and Ψ[·] :K → C1[0,T] can be described explicitly.
SourceApplied Mathematics and Information Sciences
- Araştırma Çıktıları / Scopus