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...

An accurate method is proposed to solve problems such as identification, analysis and optimal control using the Bernstein orthonormal polynomials operational matrix of integration. The Bernstein polynomials are first orthogonalized, normalized and then their operational matrix of integration is obtained. An example is given to illustrate the proposed method. Mathematics Subject Classification: ...

In this paper, the Legendre wavelet neural network with extreme learning machine is proposed for numerical solution of time fractional Black–Scholes model. way, operational matrix derivative based on two-dimensional derived and employed to solve European options pricing problem. This scheme converts problem into calculation a set algebraic equations. The constructed; meanwhile, algorithm adopte...

This paper is devoted to proposing an approximate numerical algorithm based on the use of state parameterization technique in order find solution optimal control problem (OCP). An explicit formula for new shifted wavelet (NSW) functions constructed. A that expresses first-order derivative NSW terms their original established. The development our suggested algorithms begins with extraction a ope...

Matrix valued functions play an important role in the development of algorithms for semidefinite programming problems. This paper studies generalized differential properties of such functions related to nonsmooth-smoothing Newton methods. The first part of this paper discusses basic properties such as the generalized derivative, Rademacher’s theorem, B-derivative, directional derivative, and se...

Matrix-valued functions play an important role in the development of algorithms for semidefinite programming problems. This paper studies generalized differential properties of such functions related to nonsmooth-smoothing Newton methods. The first part of this paper discusses basic properties such as the generalized derivative, Rademacher’s theorem, -derivative, directional derivative, and sem...

one of the problems in the ground-based circular synthetic aperture radar is the dependence of the azimuth resolution to the antenna rotation radius and operational limitation of increasing it. to enhance the image quality in azimuth, model-based image formation through three methods: matched filter, inverse filter and optimum filter is suggested and analyzed. for the purpose of comparison, thr...

In this article, the fractional-order differential equation of particle sedimentation was obtained. It considers Basset force’s fractional origin and contains Riemann–Liouville integral rewritten as a Grunwald–Letnikov derivative. As result, general solution proposed found analytically. The belonging to real range values strictly theoretically proven. obtained validated on particular analytical...

In this paper, we first address the general fractional integrals and derivatives with Sonine kernels that possess integrable singularities of power function type at point zero. Both particular cases compositions these operators are discussed. Then proceed a construction an operational calculus Mikusi\'nski for kernels. This is applied analytical treatment some initial value problems differentia...