The Schr\"odinger equation iβtΟβu(x,t)βuxxβ(x,t)=p(t)q(x)+f(x,t) ( 0<tβ€T,0<Ο<1), with the Riemann-Liouville derivative is
considered. An inverse problem is investigated in which, along with u(x,t),
also a time-dependent factor p(t) of the source function is unknown. To solve
this inverse problem, we take the additional condition B[u(β ,t)]=Ο(t) with an arbitrary bounded linear functional B. Existence and
uniqueness theorem for the solution to the problem under consideration is
proved. Inequalities of stability are obtained. The applied method allows us to
study a similar problem by taking instead of d2/dx2 an arbitrary elliptic
differential operator A(x,D), having a compact inverse.Comment: Schrodinger type equation