| Issue |
Math. Model. Nat. Phenom.
Volume 13, Number 1, 2018
Theory and applications of fractional differentiation
|
|
|---|---|---|
| Article Number | 13 | |
| Number of page(s) | 17 | |
| DOI | https://doi.org/10.1051/mmnp/2018002 | |
| Published online | 26 February 2018 | |
Numerical and analytical solutions of nonlinear differential equations involving fractional operators with power and Mittag-Leffler kernel
1
Universidad Autónoma de la Ciudad de México,
Prolongación San Isidro 151, Col. San Lorenzo Tezonco, Del. Iztapalapa,
C.P. 09790
México D.F., Mexico
2
CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira,
C.P. 62490
Cuernavaca,
Morelos, Mexico
* Corresponding author: jgomez@cenidet.edu.mx
Received:
5
September
2017
Accepted:
24
September
2017
Analytical and numerical simulations of nonlinear fractional differential equations are obtained with the application of the homotopy perturbation transform method and the fractional Adams-Bashforth-Moulton method. Fractional derivatives with non singular Mittag-Leffler function in Liouville-Caputo sense and the fractional derivative of Liouville-Caputo type are considered. Some examples have been presented in order to compare the results obtained, classical behaviors are recovered when the derivative order is 1.
Mathematics Subject Classification: 30.02.Jr / 60.02.Cb / 60.02.Lj
Key words: Fractional calculus / nonlinear fractional differential equations / homotopy perturbation transform method / fractional derivative with nonsingular Mittag-Leffler kernel
© EDP Sciences, 2018
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