Fractional vector calculus and fluid mechanics

• Main Authors: Lazopoulos Konstantinos A., Lazopoulos Anastasios K.
• Format: Article
• Language: English
• Published: De Gruyter 2017-04-01
• Series: Journal of the Mechanical Behavior of Materials
• Subjects: fractional continuum mechanics; fractional darcy flow; fractional derivative; fractional fluid mechanics; fractional geometry; fractional navier stokes equations; fractional newtonian fluids
• Online Access: https://doi.org/10.1515/jmbm-2017-0012

Basic fluid mechanics equations are studied and revised under the prism of fractional continuum mechanics (FCM), a very promising research field that satisfies both experimental and theoretical demands. The geometry of the fractional differential has been clarified corrected and the geometry of the fractional tangent spaces of a manifold has been studied in Lazopoulos and Lazopoulos (Lazopoulos KA, Lazopoulos AK. Progr. Fract. Differ. Appl. 2016, 2, 85–104), providing the bases of the missing fractional differential geometry. Therefore, a lot can be contributed to fractional hydrodynamics: the basic fractional fluid equations (Navier Stokes, Euler and Bernoulli) are derived and fractional Darcy’s flow in porous media is studied.