This paper investigates the instability of an isotropic, homogeneous, simply supported rectangular plate subjected to a prescribed periodic in-plane load. The material is assumed to be viscoelastic and obey the Leaderman nonlinear constitutive relation. The equation of motion is derived as a nonlinear integro-partial-differential equation, and is simplified into a nonlinear integro-differential...

A new integro-differential equation for diffuse photon density waves (DPDW) is derived within the diffusion approximation. The new equation applies to inhomogeneous bounded turbid media. Interestingly, it does not contain any terms involving gradients of the light diffusion coefficient. The integro-differential equation for diffusive waves is used to develop a 3D-slice imaging algorithm based t...

We derive heuristically an integro-differential equation, as well as a shell model, governing the dynamics of the Lowest Landau Level equation in a high frequency regime.

This paper deals with the exponential stability of a class of nonlinear delay-integrodifferential equations of the form ẋ(t) = f ( t, x(t), x(t − τ1(t)), ∫ t t−τ2(t) g(t, s, x(s))ds ) , t ≥ t0, where τi(t) > 0 for i = 1, 2 and t ≥ t0. The stability relation between ordinary and delay-integro-differential equations is given. It is shown under some suitable conditions that a delay-integro-differe...

in this paper, we apply the local fractional laplace transform method (or yang-laplace transform) on volterra integro-differential equations of the second kind within the local fractional integral operators to obtain the analytical approximate solutions. the iteration procedure is based on local fractional derivative operators. this approach provides us with a convenient way to find a solution ...

In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized characterization Theorem. Then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. Here neural network is considered as a part of large eld called ne...

We consider nonlinear integro-differential equations like the ones that arise from stochastic control problems with purely jump Lévy processes. We obtain a nonlocal version of the ABP estimate, Harnack inequality, and interior C 1; ̨ regularity for general fully nonlinear integro-differential equations. Our estimates remain uniform as the degree of the equation approaches 2, so they can be seen ...

In this paper we consider a risk model with two classes of insurance risks in the presence of multiple thresholds. We assume that the two claim counting processes are, respectively, Poisson and Sparre Andersen with generalized Erlang(2) claim inter-arrival times. We derive an integro-differential system for the Gerber-Shiu functions for surplus-dependent premium rates and a piecewise integro-di...