Linear higher-order fractional differential and integral equations

We study the equivalences and implications between linear (or homogeneous) nth order fractional differential equations (FDEs) integral in spaces L1(a,b) C[a,b] when n≥ 2. establish equivalence of IVP FDE subject to initial condition u(i)(a)=ui for i {0,1,...,n-1} n≥2. The difficulty is that known conditions such first FDEs are not sufficient with In this article we provide additional ensure particular, obtain under which solutions FDEs. These results keys further studying existence nonnegative boundary value problems nonlinear This done via corresponding by topological methods as Banach contraction principle, fixed point index theory, degree theory.