Efficient analytical approach to solve system of BVPs associated with fractional obstacle problem

The general obstacle framework has found applications in steady state fluid interaction, thin-plate fluid dynamics, study of minimal surfaces, control theory, elasto-statics, etc. The obstacle problem involving the fractional operator indeed appears in many contexts, such as in the analysis of anomalous diffusion, in the quasi-geostrophic flow problem, and in pricing of American options regulated by assets evolving in relation to jump processes; these notable applications in financial mathematics and physics made the obstacle problem very important in recent times. In this work, we present a fractional contact problem in which derivative of fractional order in the sense of Caputo is involved. Using the penalty function method, we degenerate it into a system of fractional boundary value problems with known obstacle. We apply the variational iteration method (VIM) for finding the series solution of these fractional BVPs. In order to ensure the accuracy and convergence of solution, residual errors of the solutions for various values of fractional parameters are plotted. The quite accurate results show that variational iteration method is one of the highly potential and robust method for solving fractional BVPs.