Lagrangian for the Convection-Diffusion Equation
Jacky Cresson (LMA-PAU), Isabelle Greff (LMA-PAU), Pierre Inizan, (IMCCE)
TL;DR
This paper develops a fractional variational formulation for the convection-diffusion equation using asymmetric fractional calculus, providing a new mathematical framework for analyzing such equations with constant coefficients.
Contribution
It introduces a novel fractional Lagrangian variational approach specifically for the convection-diffusion equation with constant coefficients.
Findings
Derivation of a fractional Lagrangian for the convection-diffusion equation
Application of asymmetric fractional calculus in variational principles
Potential for new analytical and numerical methods
Abstract
Using the asymmetric fractional calculus of variations, we derive a fractional Lagrangian variational formulation of the convection-diffusion equation in the special case of constant coefficients.
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