Minimizing a class of polyconvex functionals involving Caputo derivatives

Abstract

Abstract In this article, we establish the existence of multiple, infinitely many, nontrivial solutions to a class of nonlinear fractional elliptic systems in fractional variational form subject to pointwise gradient constraint and pure Dirichlet-type boundary conditions. We use a topological class of maps referred to as generalized twists and examine them in connection with the later system of fractional Euler-Lagrange equations and prove the existence of a countably infinite of topologically distinct twisting solutions to this system.

Keywords

• Twist maps
• Fractional calculus
• Euler-Lagrange equation
• Polyconvexity
• Natural boundary conditions