A novel computational framework to approximate analytical solution of nonlinear fractional elastic beam equation

Abstract

Abstract. In this paper, the generalized travelling solutions of the nonlinear fractional beam equation is investigated by means of the homotopy perturbation method. The fractional derivative is described in the Caputo sense. The reliability and potential of the proposed approach, which is based on joint Fourier-Laplace transforms and the homotopy perturbation method, will be discussed. The solutions can be approximated via an analytical series solution. Moreover, the convergence and stability of the proposed approach for this equation is investigated, and the results reveal that the proposed scheme is very e ective and promising.

Intelligent real-time monitoring of Computer Numerical Control tool wear based on a fractional-order chaotic self-synchronization system

“…This method was proposed by Hu and He 24 who also used the Fornberg–Whitham equation for all kinds of physical and engineering problems, 24 improvement of the Riemann–Liouville derivative, 25 and many other applications. 26,27…”