fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. for that reason, we need a reliable and efficient technique for the solution of fractional differential equations. the aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

optimal reactive power dispatch (orpd) is a multi-variable problem with nonlinear constraints and continuous/discrete decision variables. due to the stochastic behavior of loads, the orpd requires a probabilistic mathematical model. in this paper, monte carlo simulation (mcs) is used for modeling of load uncertainties in the orpd problem. the problem is formulated as a nonlinear constrained mul...

Fractional calculus has been used to model the physical and engineering processes that have found to be best described by fractional differential equations. For that reason, we need a reliable and efficient technique for the solution of fractional differential equations. The aim of this paper is to present an analytical approximation solution for linear and nonlinear multi-order fractional diff...

Modelling and forecasting Stock market is a challenging task for economists and engineers since it has a dynamic structure and nonlinear characteristic. This nonlinearity affects the efficiency of the price characteristics. Using an Artificial Neural Network (ANN) is a proper way to model this nonlinearity and it has been used successfully in one-step-ahead and multi-step-ahead prediction of di...

Optimal Reactive Power Dispatch (ORPD) is a multi-variable problem with nonlinear constraints and continuous/discrete decision variables. Due to the stochastic behavior of loads, the ORPD requires a probabilistic mathematical model. In this paper, Monte Carlo Simulation (MCS) is used for modeling of load uncertainties in the ORPD problem. The problem is formulated as a nonlinear constrained mul...

In this paper, the efficient multi-step differential transform method (EMsDTM) is applied to get the accurate approximate solutions for strongly nonlinear duffing oscillator. The main improvement of EMsDTM which is to reduce the number of arithmetic operations, is thoroughly investigated and compared with the classic multi-step differential transform method (MsDTM). To illustrate the applicabil...

This paper deals with leader-following and leaderless consensus problems of high-order multi-input/multi-output (MIMO) multi-agent systems with unknown nonlinear dynamics in the presence of uncertain external disturbances. The agents may have different dynamics and communicate together under a directed graph. A distributed adaptive method is designed for both cases. The structures of the contro...

The Kernel based Nonlinear Subspace (KNS) method is proposed for multi-class pattern classi cation. This method consists of the nonlinear transformation of feature spaces de ned by kernel functions and subspace method in transformed high-dimensional spaces. The Support Vector Machine, a nonlinear classi er based on a kernel function technique, shows excellent classi cation performance, however,...

The functional form representation of input-output relationship through Volterra series provides a structured mathematical platform for the study of nonlinear systems. It employs multi-dimensional kernels, which upon convolution with the applied excitation forces, express system response in the form of a power series. Frequency domain transforms of these multi-dimensional kernels provide higher...