In this chapter, we focus on the analysis and application of model reduction techniques for networks involving the transfer, flow, or transport of quantities along their connections. Specifically, we formally introduce how these networks give rise to fractional-order operators, providing a streamlined method for studying large-scale, complex physical systems. Finally, based on this physical interpretation of fractional-order operators, we present a preliminary study on the application of fractional calculus in modeling the cardiovascular system.

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From Self-similar Networks to Fractional Systems. A Formal Introduction

  • Jesús Enrique Escalante-Martínez,
  • Adrian-Josue Guel-Cortez,
  • Liliana Félix,
  • César Fernando Méndez-Barrios

摘要

In this chapter, we focus on the analysis and application of model reduction techniques for networks involving the transfer, flow, or transport of quantities along their connections. Specifically, we formally introduce how these networks give rise to fractional-order operators, providing a streamlined method for studying large-scale, complex physical systems. Finally, based on this physical interpretation of fractional-order operators, we present a preliminary study on the application of fractional calculus in modeling the cardiovascular system.