and Applied Analysis 3 Define a function m t by m t v t ∫ t 0 g s v s ds v t ∫ t 0 g s ds, 2.5 then m 0 v 0 u0, v t ≤ m t , v′ t ≤ f t m t , 2.6 m′ t 2g t v t v′ t ( 1 ∫ t 0 g s ds ) ≤ m t [ 2g t f t ( 1 ∫ t 0 g s ds )] . 2.7 Integrating 2.7 from 0 to t, we have m t ≤ u0 exp (∫ t 0 ( 2g s f s ( 1 ∫ s 0 g σ dσ )) ds ) . 2.8 Using 2.8 in 2.6 , we obtain v′ t ≤ u0f t exp (∫ t 0 ( 2g s f s ( 1 ∫ s ...

The relations between wavelet shrinkage and nonlinear diffusion for discontinuity-preserving signal denoising are fairly well-understood for singlescale wavelet shrinkage, but not for the practically relevant multiscale case. In this paper we show that 1-D multiscale continuous wavelet shrinkage can be linked to novel integrodifferential equations. They differ from nonlinear diffusion filtering...

Abstract. In this paper, a method is employed to approximate the solution of two-dimensional nonlinear Volterra integro-differential equations (2DNVIDEs) with supplementary conditions. First, we introduce twodimensional Legendre polynomials, then convert 2DNVIDEs to the two-dimensional linear Volterra integrodifferential equations (2DLVIDEs). Using this properties and collocation points, reduce...

We introduce a one parameter family of non-linear, non-local integrodifferential equations and its limit equation. These equations originate from a derivation of the linear Boltzmann equation using the framework of bosonic quantum field theory. We show the existence and uniqueness of strong global solutions for these equations, and a result of uniform convergence on every compact interval of th...

We investigate the relations between wavelet shrinkage and integrodifferential equations for image simplification and denoising in the discrete case. Previous investigations in the continuous one-dimensional setting are transferred to the discrete multidimentional case. The key observation is that a wavelet transform can be understood as derivative operator in connection with convolution with a...

In this paper, we discuss a class of fractional semilinear integrodifferential equations mixed type with delay. Based on the theories resolvent operators, measure noncompactness, and fixed point theorems, establish existence uniqueness global mild solutions for equations. An example is provided to illustrate application our main results.

In a previous article [1] we have shown how one can employ Artificial Neu-ral Networks (ANNs) in order to solve non-homogeneous ordinary and partial differential equations. In the present work we consider the solution of eigen-value problems for differential and integrodifferential operators, using ANNs. We start by considering the Schrödinger equation for the Morse potential that has an analyt...

Consider the singular perturbation problem for εu(t; ε) + u(t; ε) = Au(t; ε) + ∫ t 0 K(t− s)Au(s; ε) ds+ f(t; ε) , where t ≥ 0, u(0; ε) = u0(ε), u (0; ε) = u1(ε), and w(t) = Aw(t) + ∫ t 0 K(t− s)Aw(s)ds+ f(t) , t ≥ 0 , w(0) = w0 , in a Banach space X when ε → 0. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and K(t) is a bounded linear opera...

This paper addresses the issue of approximate controllability for a class of control systemwhich is represented bynonlinear fractional integrodifferential equations with nonlocal conditions. By using semigroup theory, p-mean continuity and fractional calculations, a set of sufficient conditions, are formulated and proved for the nonlinear fractional control systems. More precisely, the results ...