MULTIVALUED FRACTIONAL DIFFERENTIAL-EQUATIONS

In this paper we study the Cauchy problem of the multivalued fractiona l differential equation d(proportional to) x(t)/dt(proportional to) is an element of F(t, x(t)) a.e. on I = [0, T], alpha is an element of R (+) as a consequent result of the study of the Cauchy problem of the f ractional differential equation d(proportional to) x(t)/dt(proportiona l to) = f(t, x(t)), t is an element of I, alpha is an element of R(+) in the Banach space E, where F(t, x(t)) is a set-valued function defin ed on I x E. The existence and some other properties of the solution w ill be proved. Continuation of the problem to the Cauchy problem of th e multivalued differential equation d(n)x(t)/dt(n) is an element of F( t, x(t)) a.e. on I, and n = 1, 2,..., will be established.