Abstract In this article, first, we present an example of fuzzy normed space by means the Mittag-Leffler function. Next, extend concept to matrix valued and also introduce a class control functions stabilize nonlinear ϕ -Hadamard fractional Volterra integro-differential equation. sense, investigate Ulam–Hyers–Rassias stability for kind equations in Banach space. Finally, as application, using f...

Conventional Volterra series model is hardly applied to engineering practice due to its parametric complexity and estimation difficulty. To solve this problem, nonlinear system identification using reduced complexity Volterra models is proposed. Since the nonlinear components often play a secondary role compared to the dominant, linear component of the system, they spend the most of identificat...

Abstract In this work we study the space of derivations non-degenerate evolution algebras. We improve some results obtained recently in literature and, as a consequence, advance description for n -dimensional Volterra addition, introduce notion loop an algebra and analyze under which conditions set loops is invariant change basis.

This paper presents a comparison between variational iteration method (VIM) and modfied variational iteration method (MVIM) for approximate solution a system of Volterra integral equation of the first kind. We convert a system of Volterra integral equations to a system of Volterra integro-di®erential equations that use VIM and MVIM to approximate solution of this system and hence obtain an appr...

The purpose of this note is to prove an abstract operator version of certain existence theorems for differential and Volterra integral equations which deal with stability properties of solutions. We will do this in such a way that the results unify, as well as generalize, many of the basic theorems concerning stability of such equations. Thus, our main result(Theorem2)is an abstract version of ...

τ∗ = inf { t∗ ≤ t ≤ T | b1(t) ≤ S t −B t ≤ b2(t) } where t∗ ∈ [0, T ) and the functions t 7→ b1(t) and t 7→ b2(t) are continuous on [t∗, T ] with b1(T )=0 and b2(T )=1/2μ . If μ > 0 then b1 is decreasing and b2 is increasing on [t∗, T ] with b1(t∗) = b2(t∗) when t∗ 6= 0 . Using local time-space calculus we derive a coupled system of nonlinear Volterra integral equations of the second kind and s...

This is a short tutorial on Volterra and Wiener series applications to modelling of nonlinear systems and phenomena, and also a survey of the recent achievements in this area. In particular, we show here how the philosophies standing behind each of the above theories differ from each other. On the other hand, we discuss also mathematical relationships between Volterra and Wiener ker...

In this paper, we present a new kind of the bilinear systems in the form of state space model. The evolution of this system depends on the product of state vector by its self. The well known Lotak Volterra and Lorenz models are special cases of this new model. We also present here a generalization of Kalman filter which is suitable to work with the new bilinear model. An application to real mea...

A class of single input single output bilinear systems described by their input–output difference equation is considered. A simple expression for the Volterra kernels of the system is derived in terms of the coefficients of difference equation. An algorithm, based on the singular value decomposition of a generalized Hankel matrix, is also developed. The algorithm is then used to find a reduced-...