Parameter identification in fractional differential equations

Abstract

This article investigates the fractional derivative order identification, the coefficient identification, and the source identification in the fractional diffusion problems. If 1 < α < 2, we prove the unique determination of the fractional derivative order and the diffusion coefficient p(x) by ∫0tu(0,s)ds, 0 < t < T for one-dimensional fractional diffusion-wave equations. Besides, if 0 < α < 1, we show the unique determination of the source term f(x,y) by U(0,0,t), 0 <t <T for two-dimensional fractional diffusion equations. Here, α denotes the fractional derivative order over t.