Fractional Boundary Layer Flow: Lie Symmetry Analysis and Numerical Solution

Alessandra Jannelli () and Maria Paola Speciale
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Alessandra Jannelli: Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 98166 Messina, Italy
Maria Paola Speciale: Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 98166 Messina, Italy

Mathematics, 2024, vol. 12, issue 2, 1-10

Abstract: In this paper, we present a fractional version of the Sakiadis flow described by a nonlinear two-point fractional boundary value problem on a semi-infinite interval, in terms of the Caputo derivative. We derive the fractional Sakiadis model by substituting, in the classical Prandtl boundary layer equations, the second derivative with a fractional-order derivative by the Caputo operator. By using the Lie symmetry analysis, we reduce the fractional partial differential equations to a fractional ordinary differential equation, and, then, a finite difference method on quasi-uniform grids, with a suitable variation of the classical L1 approximation formula for the Caputo fractional derivative, is proposed. Finally, highly accurate numerical solutions are reported.

Keywords: fractional Sakiadis flow; nonlinear boundary value problem on semi-infinite domain; Caputo operator; Lie symmetry analysis; quasi-uniform grid; finite difference schemes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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