Integro-differential Volterra Equation with delay term

Abstract

"As part of this master's thesis, we focus on a new equation integro-di erential tion of Volterra with a delay term: ∀t ∈ [a; b], u(t) = int^α(t)_aN(t, s, u(s), u′(s))ds + f(t), Our main objective is to prove the existence and the uniqueness of the solution of this equation using a Picard sequence, a method commonly used in the analysis of integral and integro-differential equations. Moreover, we propose to use a Nystrem method to construct a numerical approximation of the solution analytic."