Fractional Differential Equations and Travelling Waves

Abstract

In this thesis, we will study certain classes of differential equations of fractional order in the sense of Caputo and some other classes in the conformable fractional sense of Khalil. We use the theory of xed points on Banach spaces. We use also the theory of nonlinear operators and the theory of inequalities to study the existence, uniqueness and stability in the sense of Ulam-Hyers. We illustrate the main results with several academic applications. We will also try as far as possible to deal with problems inspired by physics. We devote a nal part of our thesis project to physical applications, we will be interested to study some important classes of EDF solutions that are called traveling wave solutions". Such classes of solutions are very important in applications because they can be used to model the spread of epidemics. We use numerical methods, such as: Tanh Method to obtain and calculate these important classes of solutions.