this article is devoted to study of the autoconvolution equations and generalized mittag-leffler functions. these types of equations are given in terms of the laplace transform convolution of a function with itself. we state new classes of the autoconvolution equations of the first kind and show that the generalized mittag-leffler functions are solutions of these types of equations. in view of ...

some scientists are interesting to study in area of harvested ecological modelling. the harvested population dynamics is more realistic than other ecological models. in the present paper, some of the lotka-volterra predator-prey models have been considered. in the said models, existing species are harvested by constant or variable growth rates. the behavior of their solutions has been analyzed ...

For permanent and partially permanent, uniformly bounded Lotka-Volterra systems, we apply the Split Lyapunov function technique developed for competitive Lotka-Volterra systems to find new conditions that an interior or boundary fixed point of a Lotka-Volterra system with general species-species interactions is globally asymptotically stable. Unlike previous applications of the Split Lyapunov t...

In this study, a new application of Taylor expansion is considered to estimate the solution of Volterra-Fredholm integral equations (VFIEs) and systems of Volterra-Fredholm integral equations (SVFIEs). Our proposed method is based upon utilizing the nth-order Taylor polynomial of unknown function at an arbitrary point and employing integration method to convert VFIEs into a system of linear equ...

We propose a new class of mapping-based nonlinear quadratic Volterra filters for image enhancement. The input signal is mapped prior to filtering by a memoryless one-to-one nonlinear mapping function. The mapping function can be described by any arbitrary function and implemented by a simple look-up table. If necessary, an inverse mapping function is applied after filtering. Using this general ...

The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors decay exponentially provided that the kernel function...

In this paper, we investigate periodic solutions of linear and nonlinear discrete Volterra equations of convolution or non-convolution type with unbounded memory. For linear discrete Volterra equations of convolution type, we establish Fredholm’s alternative theorem and for equations of non-convolution type, and we prove that a unique periodic solution exists for a particular bounded initial fu...

Volterra integral equations arise in many problems pertaining to mathematical physics like heat conduction problems. Several numerical methods for approximating the solution of Volterra integral equations are known [1-10]. This paper is focused on the solution of Volterra integral equations of the second kind with weakly singular kernel via Haar function by taking advantage of the nice properti...

Here, the solution in one, two and three dimensional for the Volterra–Fredholm integral equation of the first kind is obtained in the space L2ðXÞ C1⁄20; T , T < 1. Using a numerical method the integral equation of Volterra–Fredholm becomes a linear system of Fredholm integral equation when that the kernel of Fredholm integral takes a logarithmic form, Carleman function, generalized potential fu...

The response of visual cells is a nonlinear function of their stimuli. In addition, an increasing amount of evidence shows that visual cells are optimized to process natural images. Hence, finding good nonlinear models to characterize visual cells using natural stimuli is important. The Volterra model is an appealing nonlinear model for visual cells. However, their large number of parameters an...