Chapter 2 - Preliminaries on fractional calculus

Abstract

The neutron transport equations and point reactor kinetics equations are represented with partial and ordinary differential equations of the integer order. This book is about nuclear reactor analysis with nonlocal approximation of differential equations of fractional order. The fractional calculus with more than 300 years of history is an extension of ordinary calculus. In this chapter, a brief introduction of the preliminaries on fractional calculus is presented, with the idea that the book is self-contained. Besides, the numerical approximation to solve problems in nuclear reactor analysis with models of fractional order in space and time is presented and discussed. From a physical and mathematical point of view, fractional calculus is a fundamental approach to consider nonlocal effects in space and time. Depending on the approximation of the neutron current vector, one can explore a description of noninstantaneous phenomena, that is, with memory effects.