A Comparison Study of Caputo and Atangana–Baleanu Fractional Approaches for Radiation and Magnetic Field Impact on CNT-H$$_2$$O Casson Nanofluid Across a Vertical Plate

Mahitha, Orugonda; Vijayakumar, Arun

doi:10.1007/s13369-023-08112-0

Search citation statements

Order By: Relevance

Paper Sections

Select...

The Fractional Derivatives With Mittag-leffler Kernel1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 45 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some properties and applications of the ML FD operator can be found in [24][25][26][27][34][35][36]. Now, if 0 < α < 1 then the ML FD and the associated FI operators satisfy the following relationships,…”

Section: The Fractional Derivatives With Mittag-leffler Kernelmentioning

confidence: 99%

Numerical simulation of fractional-order Duffing system with extended Mittag-Leffler derivatives

Odibat

2024

Phys. Scr.

View full text Add to dashboard Cite

In this paper, we studied the dynamics of a nonlinear fractional-order Duffing system combined with Mittag-Leffler derivatives in order to provide dynamic behaviors different from existing ones. The Mittag-Leffler derivative is a generalized version of the exponential kernel derivative. To achieve this goal, we introduced a modified extension to higher-order Mittag-Leffler derivatives to overcome the initialization problem. Moreover, we discussed some properties and relationships of the studied derivatives. Then we presented numerical schemes to handle fractional extensions of the considered oscillatory system including the Mittag-Leffler and the Caputo derivatives. Numerical simulations are carried out and the resulting simulation dynamics of the studied fractional oscillatory system are compared.

show abstract