Theorems on some families of fractional differential equations and their applications

Gülçin Bozkurt; Durmuş Albayrak; Neşe Dernek

Applications of Mathematics (2019)

  • Volume: 64, Issue: 5, page 557-579
  • ISSN: 0862-7940

Abstract

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We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for the vibration equation with fractional damping and the Bagley-Torvik equation.

How to cite

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Bozkurt, Gülçin, Albayrak, Durmuş, and Dernek, Neşe. "Theorems on some families of fractional differential equations and their applications." Applications of Mathematics 64.5 (2019): 557-579. <http://eudml.org/doc/294208>.

@article{Bozkurt2019,
abstract = {We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for the vibration equation with fractional damping and the Bagley-Torvik equation.},
author = {Bozkurt, Gülçin, Albayrak, Durmuş, Dernek, Neşe},
journal = {Applications of Mathematics},
keywords = {fractional calculus; fractional differential equation; Caputo derivative; Laplace transform},
language = {eng},
number = {5},
pages = {557-579},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Theorems on some families of fractional differential equations and their applications},
url = {http://eudml.org/doc/294208},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Bozkurt, Gülçin
AU - Albayrak, Durmuş
AU - Dernek, Neşe
TI - Theorems on some families of fractional differential equations and their applications
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 5
SP - 557
EP - 579
AB - We use the Laplace transform method to solve certain families of fractional order differential equations. Fractional derivatives that appear in these equations are defined in the sense of Caputo fractional derivative or the Riemann-Liouville fractional derivative. We first state and prove our main results regarding the solutions of some families of fractional order differential equations, and then give examples to illustrate these results. In particular, we give the exact solutions for the vibration equation with fractional damping and the Bagley-Torvik equation.
LA - eng
KW - fractional calculus; fractional differential equation; Caputo derivative; Laplace transform
UR - http://eudml.org/doc/294208
ER -

References

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