A spectral approach to analyze the nonlinear oscillatory fractional-order differential equations

Abstract

Abstract The study of complex nonlinear mathematical models of fractional-order needs more attention in recent decades due to its enormous contribution to science and technology. Herein, a combined algorithm is proposed using the Chelyshkov polynomial method (CPM) and Picard iterative (PI) scheme. The proposed Picard Chelyshkov polynomial method (PCPM) is used to attain nonlinear oscillatory problems of arbitrary orders that do not have the exact solutions in the literature. The PCPM covert the highly nonlinear fractional-order oscillatory Problems into a linear algebraic equations system. However, the Picard scheme is to tackle the nonlinearity factor that appears in the differential equations. The proposed method's performance is examined through some test problems of fractional order while authenticated via some numerical methods. A comprehensive comparative study discussed with published work to show that the presented PCPM. To summarize, a more efficient and accurate tool is found to inspect the solution of fractional-order highly nonlinear models.