Geodesic
Theorems on some families of fractional differential equations and their applications
Applications of Mathematics, Tome 64 (2019) no. 5, pp. 557-579.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

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.
DOI : 10.21136/AM.2019.0031-19
Classification : 26A33, 34A08, 44A10, 44A15
Keywords: fractional calculus; fractional differential equation; Caputo derivative; Laplace transform 
@article{10_21136_AM_2019_0031_19,
     author = {Bozkurt, G\"ul\c{c}in and Albayrak, Durmu\c{s} and Dernek, Ne\c{s}e},
     title = {Theorems on some families of fractional differential equations and their applications},
     journal = {Applications of Mathematics},
     pages = {557--579},
     publisher = {mathdoc},
     volume = {64},
     number = {5},
     year = {2019},
     doi = {10.21136/AM.2019.0031-19},
     mrnumber = {4022163},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0031-19/}
}
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
SP  - 557
EP  - 579
VL  - 64
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0031-19/
DO  - 10.21136/AM.2019.0031-19
LA  - en
ID  - 10_21136_AM_2019_0031_19
ER  - 
%0 Journal Article
%A Bozkurt, Gülçin
%A Albayrak, Durmuş
%A Dernek, Neşe
%T Theorems on some families of fractional differential equations and their applications
%J Applications of Mathematics
%D 2019
%P 557-579
%V 64
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0031-19/
%R 10.21136/AM.2019.0031-19
%G en
%F 10_21136_AM_2019_0031_19
Bozkurt, Gülçin; Albayrak, Durmuş; Dernek, Neşe. Theorems on some families of fractional differential equations and their applications. Applications of Mathematics, Tome 64 (2019) no. 5, pp. 557-579. doi : 10.21136/AM.2019.0031-19. http://geodesic.mathdoc.fr/articles/10.21136/AM.2019.0031-19/

Cité par Sources :