Chelyshkov least squares support vector regression for nonlinear stochastic differential equations by variable fractional Brownian motion.

The main aim of this study is to introduce an efficient method based on the Chelyshkov polynomials and least squares support vector regression (LS-SVR) for solving a class of nonlinear stochastic differential equations (SDEs) by variable fractional Brownian motion (VFBm). The derivative operational matrix and variable-order fractional integral operator of Chelyshkov polynomials (ChPs) are obtained. These operators, the standard Brownian motion with help of the Gauss–Legendre quadrature are applied for generating VFBm. We apply the Chelyshkov polynomials kernel and the collocation LS-SVR method for training the network. Then, the formulation of the scheme gives rise to an optimization problem. Finally, the classical optimization and Newton's iterative scheme are used to train this problem. Moreover, we discuss convergence and error analysis of mentioned scheme. In the end, to reveal the superiority and efficiency of current paper, some test problems are applied. • We combined Chelyshkov polynomials and least squares support vector regression. • We solved stochastic differential equations by variable fractional Brownian motion. • We presented a new method for generating variable fractional Brownian motion. • We convert stochastic differential equations into an optimization problem. • Convergence of the proposed scheme is discussed. [ABSTRACT FROM AUTHOR]