New Caputo fractional differential equation of higher order on unbounded interval and solvability in the Hölder space C0,q(Ω)

Abstract

We define a new Caputo fractional differential equation of higher-order on unbounded interval {(c) D(alpha)w(t) = f(t), 0 <= t < infinity, w(0)=w '(0)=w((4))(0)=w((5))(0)=& ctdot;=w((n))(0)=0, w & tprime;(0)=integral(eta)(0)(eta-s)(alpha-1)/Gamma(alpha) f(s)ds, lim(t ->infinity)(c) D(alpha-1)w(t)=w(xi),0