Fractional Order Systems and Applications in Engineering

Chapter 11: Fourth-order fractional diffusion equations: constructs and memory kernel effects

Jordan Hristov    Department of Chemical Engineering, University of Chemical Technology and Metallurgy, Sofia, Bulgaria

Abstract

We discuss time-fractional fourth-order diffusion models in two general cases: i) Models obtained by replacement of the time derivatives by different fractional operators, with singular and nonsingular memories and ii) Models developed by applying the fading memory approach (Boltzmann superposition principle). We analyze time evolution of the solution front applying the multiple integral-balance method.

Keywords

Fourth-order fractional diffusion; Memory kernel; Multiple integral-balance method

11.1 Introduction

Fourth-order diffusion ...