Finance

Derivative (finance)

Stability (learning theory)

Physics

Mathematics

Psychotherapist

Biology

Financial economics

Displacement (psychology)

Machine learning

Fractional calculus

Mathematical analysis

Order (exchange)

Psychology

Vibration

Economics

Maple

Computer science

Botany

Quantum mechanics

Applied mathematics

Mathematical Methods in the Applied Sciences

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.

On the analysis of vibration equation involving a fractional derivative with Mittag‐Leffler law