Approximating the solution of differential equations of fractional order is necessary because fractional differential equations have extensively been used in physics, chemistry as well as engineering fields. In this paper with central difference approximation and Newton Cots integration formula, we have found approximate solution for a class of boundary value problems of fractional order. Three...

InGaN based MQW solar cells have been fabricated with 4 different transparent top electrode structures: (1)- ITO 200 nm, (2)-ITO nano dots only, (3)-ITO nano dots on ITO 50 nm and (4)-ITO nano dots on ITO 100 nm. The solar cell with the ITO 50 nm on ITO nano dots under AM 1.5 conditions showed the best results: 2.3 V for V(oc), 0.69 mA/cm(2) for J(sc), 41.8% for peak EQE, and 0.91% for conversi...

The usual Weyl calculus is intimately associated with the choice of the standard symplectic structure on [Formula: see text]. In this paper we will show that the replacement of this structure by an arbitrary symplectic structure leads to a pseudo-differential calculus of operators acting on functions or distributions defined, not on [Formula: see text] but rather on [Formula: see text]. These o...

Submitted: May 27, 2013; Accepted: Jul 5, 2013; Published: Jul 22, 2013 Abstract: In this paper, we present an algorithm called the Reduced Differential Transform Method (RDTM) to obtain approximate solutions for the Fitzhugh-Nagumo (FN) equation, Ito equation and find an exact solution to nonlinear PDE. The numerical results show that this method is a powerful tool for solving nonlinear PDEs a...

The Master equation is an infinite dimensional partial differential equation in a state space comprising Euclidean vectors and probability measures. It was introduced by Lasry and Lions for the study of Mean Field Games. We derive this Master Equation from a special Ito formula based on a non-standard differential calculus for functions of probability measures. If time permits, we shall also de...

A class of nonlinear stochastic processes satysfying a Lipschitz-type strip condition and supplied by a linear output equation, is considered. Robust asymptotic (high-gain) state estimation for nonlinear stochastic processes via di erential neural networks is discussed. A new type learning law for the weight dynamics is suggested. By a stochastic Lyapunov-like analysis (with Ito formula impleme...

In view of the extensive use of stochastic integrals and stochastic differential equations in modeling of systems in engineering, and economic systems especially in mathematical finance and other applied problems, it is necessary to find whether there are good approximants to the stochastic integrals and the stochastic differential equations which can be used for simulation purposes. Some work ...

We investigate the relativistic Brownian motion in the context of Fokker-Planck equation. Due to the multiplicative noise term of the corresponding relativistic Langevin equation many Fokker-Planck equations can be generated. Here, we only consider the Ito, Stratonovich and Hänggi-Klimontovich approaches. We analyze the behaviors of the second moment of momentum in terms of temperature. We show...