Nonlinear higher order fractional terminal value problems

Abstract

Terminal value problems for systems of fractional differential equations are studied with an especial focus on higher-order systems. Discretized piecewise polynomial collocation methods are used for approximating the exact solution. This leads to solving a system of nonlinear equations. For solving such a system an iterative method with a required tolerance is introduced and analyzed. The existence of a unique solution is guaranteed with the aid of the fixed point theorem. Order of convergence for the given numerical method is obtained. Numerical experiments are given to support theoretical results.

Keywords

• terminal value problems
• systems of fractional differential equations
• existence
• regularity
• weakly singular volterra and fredholm integral equations
• piecewise polynomials collocation methods