DETERMINATION OF A TIME-DEPENDENT COEFFICIENT IN THE TIME-FRACTIONAL WAVE EQUATION WITH A NON-CLASSICAL BOUNDARY CONDITION

DETERMINATION OF A TIME-DEPENDENT COEFFICIENT IN THE TIME-FRACTIONAL WAVE EQUATION WITH A NON-CLASSICAL BOUNDARY CONDITION

I. Tekin, H. Yang

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Abstract

In this paper, an initial-boundary value problem for the time-fractional wave equation is considered. Given an additional condition, a time-dependent coe cient is determined and the existence and uniqueness theorem for small time is proved. An e - cient  nite di erence scheme for solving the inverse problem is also proposed.

Keywords

Fractional wave equation, inverse coe cient problem, existence and uniqueness, non-classical boundary condition,  nite di erence method.