Let H(B) denote the space of all holomorphic functions on the unit ball B ⊂ Cn. Let φ be a holomorphic self-map of B and g ∈ H(B). In this paper, we investigate the boundedness and compactness of the Volterra composition operator

In this paper, we prove the existence of mild solutions for the semilinear fractional order functional of Volterra-Fredholm type differential equations with impulses in a Banach space. The results are obtained by using the theory of fractional calculus, the analytic semigroup theory of linear operators and the fixed point techniques. ifx

In this paper we carefully study the analysis involved with Volterra series. We address system-theoretic issues ranging from bounds on the gain and incremental gain of Volterra series operators to the existence of Volterra series operator inverses, and mathematical topics such as the relation between Volterra series operators and Taylor series. The proofs are complete, and use only the basic fa...

Abstract This paper aims to developed a high-order and accurate method for the solution of one-dimensional Lotka-Volterra-diffusion with Numman boundary conditions. A fourth-order compact finite difference scheme spatial part combined implicit-explicit Runge Kutta in temporal are proposed. Furthermore, points discretized by using terms fourth order accuracy. key idea proposed is take full advan...

In this study, a fractional nonlinear mixed integro-differential equation (Fr-NMIDE) is presented and has general discontinuous kernel based on position time space. Conditions of the existence uniqueness solution provided through principal form integral equation, Banach fixed point theorem. After applying properties integral, Fr-NMIDE conformed to Volterra–Hammerstein (V-HIE) second kind, with ...

In this paper, the existence of a unique solution of Volterra-Hammerstein integral equation of the second kind (VHIESK) is proved by using Banach fixed point theorem (BFPT) in the space ] , 0 [ ) ( 2 T C L   , where  represents the domain of integration of the variable space and T is the time. Then, different kinds of projectioniteration methods (PIMs) for solving this integral equation in t...

3 Example: Differentiating the Lotka-Volterra ODE system 2 3.1 The Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 The derivatives of the Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . 3 3.3 Integration of the original and augmented Lotka-Volterra ODE system with the Runge-Kutta method . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

For the past two decades, the Volterra series reduced-order modeling approach has been successfully used for the purpose of flutter prediction, aeroelastic control design, and aeroelastic design optimization. The approach has been less successful, however, when applied to other important aeroelastic phenomena, such as aerodynamically induced limit-cycle oscillations. Similar to the Taylor serie...

We study the difference-difference Lotka-Volterra equations in p-adic number space and its p-adic valuation version. We point out that the structure of the space given by taking the ultra-discrete limit is the same as that of the p-adic valuation space. Since ultra-discrete limit can be regarded as a classical limit of a quantum object, it implies that a correspondence between classical and qua...