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A Review of Lagrangian Formalism in Biology: Recent Advances and Perspectives

Autor: Pham, Diana T., Musielak, Zdzislaw E.

The Lagrangian formalism has attracted the attention of mathematicians and physicists for more than 250 years and has played significant roles in establishing modern theoretical physics. The history of the Lagrangian formalism in biology is much shor

Externí odkaz: http://arxiv.org/abs/2408.10834

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Higher Order Fractal Differential Equations

Autor: Golmankhaneh, Alireza Khalili, Depollier, Claude, Pham, Diana

This paper provides a summary of the fractal calculus framework. It presents higher-order homogeneous and nonhomogeneous linear fractal differential equations with $\alpha$-order. Solutions for these equations with constant coefficients are obtained

Externí odkaz: http://arxiv.org/abs/2404.00452

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Lagrangian Formalism in Biology: II. Non-Standard and Null Lagrangians and their Role in Population Dynamics

Autor: Pham, Diana T., Musielak, Zdzislaw E.

Non-standard Lagrangians do not display any discernible energy-like terms, yet they give the same equations of motion as standard Lagrangians, which have easily identifiable energy-like terms. A new method to derive non-standard Lagrangians for secon

Externí odkaz: http://arxiv.org/abs/2301.09419

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Spectra of Reduced Fractals and Their Applications in Biology

Autor: Pham, Diana T., Musielak, Zdzislaw E.

Publikováno v: Fractal Fract. 2023, 7, 28

Fractals with different levels of self-similarity and magnification are defined as reduced fractals. It is shown that spectra of these reduced fractals can be constructed and used to describe levels of complexity of natural phenomena. Specific applic

Externí odkaz: http://arxiv.org/abs/2111.01719

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