In this paper, biochemical reaction problem is given in the form of a system of non-linear differential equations involving Caputo fractional derivative. The aim is to suggest an instrumental scheme to approximate the solution of this problem. To achieve this goal, the fractional derivation terms are expanded as the elements of shifted Legendre scaling functions. Then, applying operational matr...

In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...

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...

This paper analyzes a linear system of equations when the righthandside is a fuzzy vector and the coefficient matrix is a crisp M-matrix. Thefuzzy linear system (FLS) is converted to the equivalent crisp system withcoefficient matrix of dimension 2n × 2n. However, solving this crisp system isdifficult for large n because of dimensionality problems . It is shown that thisdifficulty may be avoide...

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...

In this paper, the two-dimensional triangular orthogonal functions (2D-TFs) are applied for solving a class of nonlinear two-dimensional Volterra integral equations. 2D-TFs method transforms these integral equations into a system of linear algebraic equations. The high accuracy of this method is verified through a numerical example and comparison of the results with the other numerical methods.

pollution has become a very serious threat to our environment. monitoring pollution is the rst step toward planning to save the environment. the use of dierential equations, monitoring pollution has become possible. in this paper, a ritz-collocation method is introduced to solve non-linear oscillatory systems such as modelling the pollution of a system of lakes. the method is based upon bernoul...

The current paper contributes a novel framework for solving a class of linear matrix differential equations. To do so, the operational matrix of the derivative based on the shifted Bernoulli polynomials together with the collocation method are exploited to reduce the main problem to system of linear matrix equations. An error estimation of presented method is provided. Numerical experiments are...

In this paper, the input-output behavior of a linear stable system is studied in some detail. Some results are presented to make more precise the folklore statement that outputs follow inputs for stable linear systems. Based on these results, it is also discussed how to choose an output and how to fuse a number of sensor outputs, to best trac k the input in stationarit y.