Such a type of singular systems appears in many problems of applications.
Recall that equations of type (1) with (f_{n}=0), (ninmathbb{N}_{0}), appeared in many problem books on classical analysis ([7, 24]), especially in those dealing with sequences and integrals (by using the integration in parts an integral (I_{n}) is frequently presented in terms of a linear function of (I_{n-2})).
Equilibrium problems appear in many practical problems arising, for instance, physics, engineering, game theory, transportation, economics, and network (see [2 5]).
Fractional differential equations and boundary value problems involving fractional derivatives appear in many applied problems ranging from the spring-pot model [2] to geology [3] or from nonlinear circuits [4] to alternative models to differential equations [5].
The delay effects often appear in many practical problems and may turn a well-behaved system into a wild one.
In recent years, there has been published much work concerning the wave equation with time delay effects and the delay effects often appear in many practical problems.
This system is a discrete analogue of a system of d-first-order ordinary differential equations which appear in many important problems of mechanics, physics and engineering.
Time series prediction appear in many real-world problems, e.g., financial market, signal processing, weather forecasting among others.
Nonatomic fading distributions, Lagrangian separability, and having a finite number of constraints are properties that appear in many, indeed most, problems in optimal design of wireless systems.
