INVERSE PROBLEM FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH INTEGRAL CONDITIONS

Аннотация

This paper investigates the classical solvability of an inverse boundary value problem for a
time-fractional parabolic equation involving the Caputo derivative. The temperature distribution and the
unknown time-dependent lowest-order coefficient are simultaneously determined using nonlocal integral
conditions and periodic boundary conditions. By applying the separation of variables method via a
biorthogonal system of eigenfunctions and sharp estimates of generalized Mittag-Leffler functions, the
existence and uniqueness of the classical solution in Banach spaces are established.