Publication detail

Fractional Calculus

ŠMARDA, Z. TŮMA, M. VYROUBALOVÁ, J.

Original Title

Fractional Calculus

Type

course reader

Language

English

Original Abstract

Fractional calculus is an area of mathematical analysis dealing with integration and derivation of any order. In particular, it examines the possibilities of using real and complex numbers as an order of derivatives, or integral. Specifically, we will deal with continuous dynamical systems based on the Riemann-Liouville derivative and integral and the Caputo derivative and integral. The theory is explained using a large number of solved examples. Especially, we pay attention to solution methods of fractional ordinary and functional equations based on the fractional Laplace transform and modifications of analytical methods from the theory of integer differential equations and systems. We also analyze the characteristics of fractional dynamic systems using the Laplace transform. We obtain the impulse characteristic from the non-integer operator transfer functions using Mittag-Leffler functions. A number of results are illustrated with graphical outputs.

Keywords

Differential equations; Fractional laplace transform;Caputo derivative and integral;Riemann-Liouville derivative and integral

Authors

ŠMARDA, Z.; TŮMA, M.; VYROUBALOVÁ, J.

Released

23. 8. 2023

Pages from

1

Pages to

60

Pages count

60

BibTex

@misc{BUT184443,
  author="Zdeněk {Šmarda} and Martin {Tůma} and Jana {Vyroubalová}",
  title="Fractional Calculus",
  year="2023",
  pages="1--60",
  note="course reader"
}