Application of Chelyshkov wavelets and least squares support vector regression to solve fractional differential equations arising in optics and engineering

Abstract

Fractional‐order ray equations and fractional Duffing‐van der Pol oscillator equations are relationships utilized as a reliable means of modeling some phenomena in optics and engineering. The main motivation of this study is to introduce a new hybrid technique utilizing Chelyshkov wavelets and least squares‐support vector regression (LS‐SVR) for determining the approximate solution of fractional ray equations and fractional Duffing‐van der Pol oscillator equations (D‐v POEs). With the help of the Riemann‐Liouville operator for Chelyshkov wavelets and LS‐SVR (called Chw‐Ls‐SVR), the mentioned problems transform into systems of algebraic equations. The convergence analysis is discussed. Finally, the numerical results are proposed and compared with some schemes to display the capability of the numerical technique proposed here.