Multivalued fractional differential equations

摘要

In this paper we study the Cauchy problem of the multivalued fractional differential equation dδx(t)dtδ∈ F(t,x(t))a.e. onI = [O,T], δ ∈ R+ as a consequent result of the study of the Cauchy problem of the fractional differential equation ƒdδx(t)dtδ= ƒ(t)), t ∈ I, δ ∈ R+ in the Banach space E, where F(t, x(t)) is a set-valued function defined on I × E. The existence and some other properties of the solution will be proved. Continuation of the problem to the Cauchy problem of the multivalued differential equation dnx(t)/dtn ϵ F(t, x(t)) a.e. on I, and n = 1,2,…, will be established.