On the analysis of vibration equation involving a fractional derivative with Mittag‐Leffler law
By Devendra Kumar, Jagdev Singh, Dumitru Băleanu. Mathematical methods in the applied sciences, 2019
194 citations recorded by the source corpus.
The present article deals with a fractional extension of the vibration equation for very large membranes with distinct special cases. The fractional derivative is considered in Atangana‐Baleanu sense. A numerical algorithm based on homotopic technique is employed to examine the fractional vibration equation. The stability analysis is conducted for the suggested scheme. The maple software package is utilized for numerical simulation. In order to illustrate the effects of space, time, and order of Atangana‐Baleanu derivative on the displacement, the outcomes of this study are demonstrated graphically. The results revel that the Atangana‐Baleanu fractional derivative is very efficient in describing vibrations in large membranes.
Subfields: Mechanics of Materials, Modeling and Simulation, Numerical Analysis
View Paper: https://www.semanticscholar.org/paper/57c0824bde9ea2aaf80c466d70f1f33f90ac042f
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In Mechanics of Materials
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In Numerical Analysis
Citations in the corpus
- Lyapunov functions for fractional-order systems in biology: Methods and applications (2020, background): “The authors of [37] extend the fractional vibration equation for very large membranes, with distinct special cases, by considering the Atangana–Baleanu fractional derivative.”