TITLE:
Variation of Parameters for Causal Operator Differential Equations
AUTHORS:
Reza R. Ahangar
KEYWORDS:
Nonlinear Operator Differential Equations (NODE), Variation of Parameters, Nonanticipating (Causal), Alekseev Theorem
JOURNAL NAME:
Applied Mathematics,
Vol.8 No.12,
December
29,
2017
ABSTRACT: The operator T from a domain D into the space of measurable functions is
called a nonanticipating (causal) operator if the past information is independent
from the future outputs. We will study the solution x(t) of a nonlinear
operator differential equation where its changes depends on the causal operator T, and semigroup of operator A(t), and all initial parameters (t0, x0) . The
initial information is described x(t)=φ(t) for almost all t ≤t0 and φ(t0) =φ0. We will study the nonlinear variation of parameters (NVP) for this
type of nonanticipating operator differential equations and develop Alekseev
type of NVP.