LIAPUNOV FUNCTIONALS AND STABILITY IN FRACTIONAL DIFFERENTIAL EQUATIONS

摘要

This project is devoted to developing Liapunov direct method for fractional differential equations. The method consists of constructing a system related scalar function which enables investigators to analyze the qualitative behavior of solutions of a differential equation without actually finding its solutions. We first convert a class of fractional differential equations to integral equations with singular kernels and then construct Liapunov functionals for the integral equations to deduce conditions on boundedness, stability, and Lp-solutions. It has long been our view that, since the fractional differential equation can be written as an integral equation with a completely monotone kernel, it is possible to construct a Liapunov functional that is of positive type. This is another installment supporting that belief.