Application of Fractional Calculus to Fluid Mechanics

By V. Kulish, J. Lage. 2002

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Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo–Fabrizio derivatives (2016, background): “Recently, this subject has been extended in various directions such as fractional-order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, model of neurons in biology, finance, signal processing, applied mathematics, bio-engineering, viscoelasticity, fluid mechanics, and fluid ”
Modified Galerkin algorithm for solving multitype fractional differential equations (2019, methodology): “0 (t − τ)l−α−1f (l)(τ)dτ, α > 0, t > 0, (3) where l − 1 ⩽ α < l, l ∈ N.”
A Petrov–Galerkin finite element method for variable-coefficient fractional diffusion equations (2015, methodology): “Let Kh : [0, 1] → R be a piecewise quadratic spline approximation to or a piecewise cubic Hermite interpolation of K on the uniform partition on [0, 1].”
GEGENBAUER WAVELETS OPERATIONAL MATRIX METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS (2015, methodology): “Introduction Fractional differential equation is the generalization of the ordinary differential equation and is used to model the problems in many areas of science and engineering such as fluid mechanics [19], dynamic of viscoelastic materials [20], biosciences [23], electromagnetism [15] and conti”