What question did this study set out to answer?

This research aims to extend the concept of deformable derivatives to multivariable functions and higher-order derivatives.

A deformable derivative approach to Euler’s theorem for homogeneous functions and its extension to higher order partial derivatives

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Randomized trial extends deformable derivatives to multivariable functions, suggesting efficient analytic tools.

This research aims to extend the concept of deformable derivatives to multivariable functions and higher-order derivatives.
Defined partial deformable derivatives for multivariable functions in coordinate directions.
Validated findings through several test functions and examples.
Developed higher-order Euler-type theorem in the context of classical homogeneity.
Successfully extended the deformable derivative to second-order, yielding new Euler-type theorems.
Demonstrated smooth convergence of deformable Euler theorem to classical results.
Provided a computationally efficient identity for homogeneous functions, enhancing analytical capability.

Naidu et al. (2026) studied this question.

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