In this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. We approximate the exact solution by use of Radial Basis Function(RBF) collocation method. This techniqueplays an important role to reduce a fractional dierential equation to a system of equations. The numerical results demonstrate the accuracy and ability of this me...

This paper reports on an experiment investigating the effects of different kinds of computer-based visualizations on the acquisition of problem-solving skills in the domain of probability theory. Learners received either purely text-based worked examples, text plus an instruction to mentally imagine the examples contents, or the possibility of retrieving either static pictures or concrete anima...

The aim of this note is to prove a new discrepancy principle. The advantage of the new discrepancy principle compared with the known one consists of solving a minimization problem (see problem (2) below) approximately, rather than exactly, and in the proof of a stability result. To explain this in more detail, let us recall the usual discrepancy principle, which can be stated as follows. Consid...

The present study aims at indicating the existence and uniqueness result of system in extended colombeau algebra. The Caputo fractional derivative is used for solving the system of ODEs. In addition, Riesz fractional derivative of  Colombeau generalized algebra is considered. The purpose of introducing Riesz fractional derivative is regularizing it in Colombeau sense. We also give a solution to...

We consider parameter estimation of ordinary differential equation (ODE) models from noisy observations. For this problem, one conventional approach is to fit numerical solutions (e.g., Euler, Runge--Kutta) ODEs data. However, such a method does not account for the discretization error in and has limited accuracy. In study, we develop an that quantifies based on The key idea model as random var...

Consider an operator equation F(u)=0 in a Hilbert space H and assume that this equation is solvable. Let us call the problem of solving this equation ill-posed if the operator F ′(u) is not boundedly invertible, and well-posed otherwise. A general method, Dynamical Systems Method (DSM), for solving linear and nonlinear illposed problems in H is presented. This method consists of the constructio...

in this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. we approximate the exact solution by use of radial basis function(rbf) collocation method. this techniqueplays an important role to reduce a fractional dierential equation to a system of equations. the numerical results demonstrate the accuracy and ability of this me...

We propose a new perspective for solving systems of nonlinear equations by viewing them as a multiobjective optimization problem where every equation represents an objective function whose goal is to minimize the difference between the rightand left-hand side of the corresponding equation of the system. An evolutionary computation technique is suggested to solve the problem obtained by transfor...

Blind source separation technique separates mixed signals blindly without any information on the mixing system. In this paper, we have used two evolutionary algorithms, namely, genetic algorithm and particle swarm optimization for blind source separation. In these techniques a novel fitness function that is based on the mutual information and high order statistics is proposed. In order to evalu...