Intégrales et Dérivées d Ordre Arbitraire

Abstract

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.