Abstract

We prove the existence of mild solutions for the multi-term time-fractional order abstract differential equation D(t)(alpha+1)u(t) + c(1)D(t)(beta 1)u(t) + ... + c(d)D(t)(beta k)u(t) = Au(t) + D-t(alpha-1) f(t, u(t)), t is an element of [0, 1], with nonlocal initial conditions, where A is the generator of a strongly continuous cosine function, 0 < alpha <= beta(d) <= ... <= beta(1) <= 1 and c(k) >= 0 for k = 1, ..., d.