Existence et unicité des solutions des équations différentielles semi-linéaires d’ordre fractionnaire

Abstract

This dissertation studies the existence and uniqueness of mild solutions for semi- linear fractional differential equations with finite and infinite delay in the framework of the Riemann–Liouville fractional derivative. Banach’s Fixed Point Theorem is used to establish uniqueness, while the Leray–Schauder nonlinear alternative pro- vides existence results. The theory is illustrated by a tumor growth model and an infinite-memory viscoelastic plate model.