Abstract: In this paper, Laplace decomposition method is developed to solve linear and nonlinear fractional integrodifferential equations. The proposed method is based on the application of Laplace transform to nonlinear fractional integro-differential equation. The nonlinear term can easily be handled with the help of Adomian polynomials. The fractional derivative is described in the Caputo se...

We review here the development of the general formalism for the study of fermion propagation in the presence of stochastic media. This formalism allows the systematic derivation of evolution equations for averaged quantities as survival probabilities and higher order distribution moments. The formalism equally applies to any finite dimensional Schrödinger equation in the presence of a stochasti...

Anisotropic strain gradient elasticity theory is applied to the solution of a mode III crack in a functionally graded material. The theory possesses two material characteristic lengths, , and ,8, which describe the size scale effect resulting from the underlining microstructure, and are associated to volumetric and surface strain energy, respectively. The governing differential equation of the ...

Motivated by recent experiments, we calculate particle emission from a Bose-Einstein condensate trapped in single deep well of one-dimensional lattice when the interaction strength is modulated. In addition to pair emission, which has been widely studied, observe single-particle emission. Within linear response, are able write closed-form expressions for rates and reduce integrals. The full non...

Abstract The purpose of this work is to investigate a novel class noninstantaneous impulsive stochastic integrodifferential equations (SIDEs) driven by Brownian motion and Rosenblatt process. We construct new set adequate assumptions for the existence uniqueness mild solutions using analysis, analytic semigroup theory, integral equation fixed point methodology. Additionally, we study asymptotic...