In this paper, the Bagley-Torvik equation is constructed. A model approach based on non-polynomial numerical methods spline interpolation is developed to solve some problems. We show that the approximate solutions of such problems obtained by the numerical algorithm developed using non-polynomial spline interpolation functions are better than those produced by other numerical methods. The aim o...

In this paper, we formulate an efficient algorithm based on a new iterative method for the numerical solution of Bagley-Torvik equation. The fractional differential equation arises in many areas applied mathematics including viscoelasticity problems and mechanics oscillation process. We construct derivatives via Caputo-type operator to three-step using MAPLE 18 software package. further investi...

Abstract The article contains the comparative use analysis of fractional derivative three types (Riemann -Liouville, Caputo and model) at Begley -Torvik equation when modeling deformation strength characteristics polymer concrete. We also consider how to obtain a solution initial value problem for model using recurrent kernels sequence. Further, correctness is substantiated establishing type or...

Local polynomial smoother (LPS) is a weighted local least-squares nonparametric method. It provides a local Taylor series fit of the data at any location and can be directly used in a differential equation to provide a numerical scheme. In this article, we introduce this new nonparametric idea based on local polynomial smoother, for acquiring the numerical solution of the Bagley-Torvik fraction...