Résumé:
In this thesis, we are concerned with integrals and derivaitves of arbitrary order.We begin
by studing a boundary value problem of fractional order derivaitve in the sens of Caputo
such that its initiale conditions contain some RL integrals.
Then, we investigate the di¤erential systems using Caputo approch in the case where the
conditions may contain some RL integrals. We present recent results for some high order
di¤erential systems with nonlinearities that contain some derivatives in the sens of Caputo
combined with some other conditions.
Another important class of problems will be studied in this project. This class involves
in nite terms of nonlinearities. The xed point theory, the fractional calculus and some
technics of functional analysis are used to prove our main results.
