Series solution to fractional contact problem using Caputo’s derivative

Open Physics

Noor Muhammad Aslam¹  Farwa Shabieh²  Rafiq Muhammad²  Kamran Muhammad²  Saeed Faisal²  Gepreel Khaled A.³  Yao Shao-Wen⁴  Ahmad Hijaz⁵ 

[1] Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, 45550, Islamabad, Pakistan;Department of Mathematics, COMSATS University Islamabad, Wah Campus, 47040,Wah cantt, Pakistan;Department of Mathematics, Faculty of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia;School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo 454000, China;Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39,00186 Roma, Italy;

关键词: fractional contact problem;    obstacle;    variational iteration method;    caputo’s fractional derivative;   

DOI  :  10.1515/phys-2021-0046

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown