Structural Stability for Fractional Differential Equations as Boundary Value Problems

Proceedings of International Conference of Numerical Analysis and Applied Mathematics, AIP Conference Proceeding, 1281(1) (2010), 1191-1194
http://dx.doi.org/10.1063/1.3497881

In this paper we aim to construct reliable numerical schemes for the approximation of solutions to fractional boundary value problems. We focus on equations of the form D*alphay(t) = f(t,y(t)), y(a) = y1, where D*alpha denotes the fractional derivative of Caputo type, the order alpha satisfies 0 < alpha < 1 and f is a suitably behaved function. We seek solutions over a finite interval [0,T] and 0 < a < T. We investigate the structural stability of the underlying problem and discuss the numerical stability of the numerical methods we construct.