Symmetry considerations for differential equation formulations from classical and fractional Lagrangians

Uchechukwu M. Opara, Festus I. Arunaye

Abstract


The utility of Noether’s classical theorem on differential equations extended to a generalized nonclassical theorem is the focus of this paper. After addressing a couple of standard related Partial Differential Equation (P.D.E.) formulations from classical Lagrangians, it culminates into a non-classical formulation of the diffusion equation in one spatial dimension from a fractional Lagrangian. Comparisons and contrasts between techniques for the classical and fractional formulations, as done here, facilitate the basic computational methods required for building analytical results. A noteworthy interface between Distribution theory, Trace theory and Lie symmetry theory is a key point of interest in this study.

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Published: 2021-12-21

How to Cite this Article:

Uchechukwu M. Opara, Festus I. Arunaye, Symmetry considerations for differential equation formulations from classical and fractional Lagrangians, J. Math. Comput. Sci., 12 (2022), Article ID 41

Copyright © 2022 Uchechukwu M. Opara, Festus I. Arunaye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

 

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