Résolution des équations aux dérivées partielles linéaires et non-linéaires moyennant des approches analytiques. Extension aux cas d’EDP d’ordre fractionnaire

Abstract

Non-linear partial differential equations of a fractional order occur naturally in different scientific fields such as physics, viscoelasticity, medicine, electrochemistry, control theory, etc. In all these areas, it is important or even necessary to find analytical or at least approximate solutions to these problems. The purpose of this thesis is to propose new analytical and numerical methods for solving non-linear partial differential equations of a temporal fractional order, where the fractional derivative is in the Caputo sense. The accuracy and effectiveness of these methods have been proven by applying them to many concrete examples