Etude d’existence et d’unicite de certaines classes d’equations differentielles fractionnaires

Abstract

In this thesis, we focus on the existence and uniqueness of positive, bounded and unbounded solutions to certain boundary value problems on the half-line for nonlinear fractional differential equations in the sense of Erdélyi–Kober and Caputo Erdélyi–Kober derivatives in Banach space. The results were proven analytically using the Banach contraction principle, Schauder and GuoKrasnosel’skii fixed point theorems, the technique of the nonlinear alternative of Leray Schauder type and the diagonalization argument method.