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Lie Symmetries With Exact Solution for Time‐Fractional Foam Drainage Equation.

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Bibliographische Detailangaben
Titel:	Lie Symmetries With Exact Solution for Time‐Fractional Foam Drainage Equation.
Autoren:	Simon, S. Gimnitz¹ (AUTHOR) gs0842@srmist.edu.in, Bira, B.¹ (AUTHOR) bibekanb@srmist.edu.in
Quelle:	Mathematical Methods in the Applied Sciences. 3/30/2025, Vol. 48 Issue 5, p5474-5482. 9p.
Schlagwörter:	INFINITESIMAL transformations, TRANSFORMATION groups, INITIAL value problems, ORDINARY differential equations, *FRACTIONAL differential equations
Abstract:	In this article, we consider a nonlinear time‐fractional foam drainage equation and investigate the behavior of fluid flow through the foam. First, we apply the symmetry analysis and obtain the infinitesimal group of transformations involving some arbitrary parameters. Further, we classify the one‐dimensional optimal algebra, and using that, we obtain the similarity variables, which consequently reduces the time fractional partial differential equation (FPDE) to fractional‐order ordinary differential equation (FODE). Next, under the invariance condition, we construct exact solution for the given model and presented graphically. Furthermore, we derive the two‐dimensional optimal systems and nonclassical symmetry for the governing equation. Finally, we study the nature of fluid flow through the foam by numerical simulation. [ABSTRACT FROM AUTHOR]
Datenbank:	Academic Search Index

Beschreibung
Abstract:	In this article, we consider a nonlinear time‐fractional foam drainage equation and investigate the behavior of fluid flow through the foam. First, we apply the symmetry analysis and obtain the infinitesimal group of transformations involving some arbitrary parameters. Further, we classify the one‐dimensional optimal algebra, and using that, we obtain the similarity variables, which consequently reduces the time fractional partial differential equation (FPDE) to fractional‐order ordinary differential equation (FODE). Next, under the invariance condition, we construct exact solution for the given model and presented graphically. Furthermore, we derive the two‐dimensional optimal systems and nonclassical symmetry for the governing equation. Finally, we study the nature of fluid flow through the foam by numerical simulation. [ABSTRACT FROM AUTHOR]
ISSN:	01704214
DOI:	10.1002/mma.10612