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Fractional Boundary Layer Flow: Lie Symmetry Analysis and Numerical Solution

Author

Listed:
  • Alessandra Jannelli

    (Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 98166 Messina, Italy
    These authors contributed equally to this work.)

  • Maria Paola Speciale

    (Department of Mathematical and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, 98166 Messina, Italy
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Alessandra Jannelli & Maria Paola Speciale, 2024. "Fractional Boundary Layer Flow: Lie Symmetry Analysis and Numerical Solution," Mathematics, MDPI, vol. 12(2), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:184-:d:1314142
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    References listed on IDEAS

    as
    1. Jannelli, Alessandra, 2024. "A finite difference method on quasi-uniform grids for the fractional boundary-layer Blasius flow," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 382-398.
    2. Iskenderoglu, Gulistan & Kaya, Dogan, 2020. "Symmetry analysis of initial and boundary value problems for fractional differential equations in Caputo sense," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    Full references (including those not matched with items on IDEAS)

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