Abstract
Abstract 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.
Highlights
Numerous issues in physics, potential theory, fluid mechanics, and economics have been transformed in variational inequality form [1]
Obstacle problem has its own importance in core domain of variational inequalities
Later on non-integer/fractional order derivatives gained immense value to portray numerous problems faced in rheology, physics, control systems, damping laws, fluid mechanics, biomathematics, computational chemistry, control theory, engineering science, and finance
Summary
Numerous issues in physics, potential theory, fluid mechanics, and economics have been transformed in variational inequality form [1]. Later on non-integer/fractional order derivatives gained immense value to portray numerous problems faced in rheology, physics, control systems, damping laws, fluid mechanics, biomathematics, computational chemistry, control theory, engineering science, and finance. Analytical and numerical schemes have been developed to solve fractional order differential equations as it is not easy to compute their exact solutions. Due to their invaluable involvement in almost every field, scientists developed many numerical as well as analytical algorithms with much stability, see. To the best of our knowledge, the analytical solution of system of fractional boundary value problems (FBVPs) using VIM has not been discussed in the literature so far.
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