in this paper, a new numerical method for solving fractional optimal control problems (focps) is presented. the fractional derivative in the dynamic system is described in the caputo sense. the method is based upon biorthogonal cubic hermite spline multiwavelets approxima-tions. the properties of biorthogonal multiwavelets are first given. the operational matrix of fractional riemann-lioville i...

In this manuscript, a numerical technique is presented for finding the eigenvalues of the regular Sturm-Liouville problems. The Chebyshev cardinal functions are used to approximate the eigenvalues of a regular Sturm-Liouville problem with Dirichlet boundary conditions. These functions defined by the Chebyshev function of the first kind. By using the operational matrix of derivative the problem ...

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

Applications of Fr?chet derivative emerge in the sensitivity analysis matrix functions. Our work extends generalized complex step approximation using computation f (A + ei?hE) as a tool to case, and combines it with finite difference formula estimate derivative. We provide numerical results for first second order exponential square root.

We consider a design problem where experimental conditions (design points Xi) are presented in the form of sequence i.i.d. random variables, generated with an unknown probability measure ?, and only given proportion ??(0,1) can be selected. The objective is to select good candidates Xi on fly maximize concave function ? corresponding information matrix. optimal solution corresponds construction...

Enamel matrix derivative Emdogain (EMD) is widely used in periodontal treatment in spite of the fact that its effect on the developing embryo has not been elucidated. The aim of this study was to investigate the teratogenic effect of EMD on the rat embryo neural crest cells. The neural crest is a unique population of cells that migrates from the dorsal neural tube along defined pathways and pro...

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...