Fixed points and fractional differential equations: Examples

摘要

We study a fractional differential equation of Caputo type by first inverting it as anintegral equation, then noting that the kernel is completely monotone, and finally transforming itinto another integral equation with a kernel which supports both contractions and compact maps.That kernel allows us to use fixed point theory to obtain qualitative properties of solutions. At theend of Section 4 we give a list of five transformations which convert challenging problems into simplefixed point problems. We treat linear, superlinear, and sublinear examples using Krasnoselskii’s fixedpoint theorem.