Open Physics (Jul 2021)

Series solution to fractional contact problem using Caputo’s derivative

  • Rafiq Muhammad,
  • Noor Muhammad Aslam,
  • Farwa Shabieh,
  • Kamran Muhammad,
  • Saeed Faisal,
  • Gepreel Khaled A.,
  • Yao Shao-Wen,
  • Ahmad Hijaz

DOI
https://doi.org/10.1515/phys-2021-0046
Journal volume & issue
Vol. 19, no. 1
pp. 402 – 412

Abstract

Read online

In this article, contact problem with fractional derivatives is studied. We use fractional derivative in the sense of Caputo. We deploy penalty function method to degenerate the obstacle problem into a system of fractional boundary value problems (FBVPs). The series solution of this system of FBVPs is acquired by using the variational iteration method (VIM). The performance as well as precision of the applied method is gauged by means of significant numerical tests. We further study the convergence and residual errors of the solutions by giving variation to the fractional parameter, and graphically present the solutions and residual errors accordingly. The outcomes thus obtained witness the high effectiveness of VIM for solving FBVPs.

Keywords