A Study on Numerical Methods for Time Fractional Partial Differential Equations with Applications in Nuclear Reactor Dynamics

Abstract

newline The main objective of this dissertation is to develop and analyze numerical methods newlineto approximate the solutions of some one or two dimensional time-fractional partial newlinedifferential equations including those arising in nuclear reactor dynamics. Moreover, newlinesome new fractional models are developed with applications in nuclear science. newlineWe start with an introduction where we introduced the basics of fractional calculus, newlinenuclear reactor theory and the fractional models that has applications in nuclear reactor newlinedynamics. In an attempt to make the thesis self-contained, some preliminary details are newlinealso included in the introduction.