Abstract
The development of a new method to solve nonlinear models and compatible with increasing the efficiency and optimizing the results with high accuracy is difficult. Herein, we developed two novel algorithms: linearized spectral method (LSM) and semi-discrete method (SDM). We successfully applied them to investigate the fractional-order MHD Jeffery fluid model's solution over a vertically moving surface with constant heat flux. The model consists of a nonlinear coupled differential equation, which is solved with proposed techniques. To attain the influence of emerging parameters on velocity and temperature distributions, emerging parameters, namely: nonlinear thermal radiation, time-dependent thermal conductivity and diffusivity, are variates for numerical values. Viable dimensionless variables are used to nondimensionalized the governing problem. Linearized spectral scheme based on function approximation and operational-matrices of fractional and integer order de-rivatives using shifted Gegenbauer polynomials (SGPs). Picard-iterative method is adopted to linearize the governing set of equations. The time-based derivative is estimated utilizing a forward difference scheme while spatial derivatives are evaluated with operational matrices' help to present the semi-discrete method. The sig-nificant part of the proposed method is to convert the highly nonlinear problems into a set of linear equations that surely help to deal efficiently. Nusselt number exhibits a direct relation with temperature ratio and heat absorption parameters. Numerical justification provided of the proposed algorithms through convergence and error bound. Furthermore, the established algorithms can inspect the accurate solution of more fractional problems which is highly nonlinear of physical nature.