Étude de l’existence, l’unicité, la positivité et la stabilité de quelques problèmes fractionnaires non linéaires

Abstract

The fixed-point principle has many applications. It is involved in the resolution of se- veral nonlinear differential equations in particular, in the study of existence and unique- ness. In our work, first we investigate the existence and uniqueness of positive solutions for a class of Caputo-Hadamard nonlinear fractional differential equations using the method of upper and lower solutions and Schauder and Banach fixed point theorems. In the second, we are interested in the study of existence and stability of Ulam-Hyers- Rassias for a class of functional differential equations involving the fractional derivative of Hilfer-Hadamard. Application of a Schauder fixed point theorem to the existence of solu- tions. Next we prove that our problem is generalized Ulam-Hyers-Rassias stable.