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FRACTIONAL DERIVATIVE AS FRACTIONAL POWER OF DERIVATIVE [PDF]
International Journal of Mathematics, 2007 Definitions of fractional derivatives as fractional powers of derivative operators are suggested. The Taylor series and Fourier series are used to define fractional power of selfadjoint derivative operator. The Fourier integrals and Weyl quantization procedure are applied to derive the definition of fractional derivative operator.
Vasily E. Tarasov
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The Fractional Orthogonal Derivative [PDF]
Mathematics, 2015 This paper builds on the notion of the so-called orthogonal derivative, where an n-th order derivative is approximated by an integral involving an orthogonal polynomial of degree n.
Enno Diekema
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On multifractality and fractional derivatives [PDF]
Journal of Statistical Physics, 2002 It is shown phenomenologically that the fractional derivative $ =D^ u$ of order $ $ of a multifractal function has a power-law tail $\propto | | ^{-p_\star}$ in its cumulative probability, for a suitable range of $ $'s. The exponent is determined by the condition $ _{p_\star} = p_\star$, where $ _p$ is the exponent of the structure function of
U. Frisch, Takeshi Matsumoto
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Fractional Derivatives and Projectile Motion [PDF]
Axioms, 2021 Projectile motion is studied using fractional calculus. Specifically, a newly defined fractional derivative (the Leibniz L-derivative) and its successor (Λ-fractional derivative) are used to describe the motion of the projectile.
Anastasios K. Lazopoulos +1 more
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Fractional Derivatives as Inverses [PDF]
Canadian Journal of Mathematics, 1989 We write formally (C, p) indicating that the integral is summable (C, p), i.e.,if this limit exists. We note here that all integrals over a finite range are taken in the Lebesgue sense, and all inversions of such iterated integrals are justifiable by Fubini's Theorem.
Godfrey L. Isaacs
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Application of Newton’s polynomial interpolation scheme for variable order fractional derivative with power-law kernel [PDF]
Scientific ReportsThis paper, offers a new method for simulating variable-order fractional differential operators with numerous types of fractional derivatives, such as the Caputo derivative, the Caputo–Fabrizio derivative, the Atangana–Baleanu fractal and fractional ...
S Naveen, V Parthiban
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On fractional angular derivative [PDF]
Kodai Mathematical Journal, 1961 Yûsaku Komatu
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Calculus of variations with fractional derivatives and fractional integrals
Applied Mathematics Letters, 2009 We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.
Ricardo Almeida, Delfim F. M. Torres
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Open Physics, 2021 In this article, thin film flow of non-Newtonian pseudo-plastic fluid is investigated on a vertical wall through homotopy-based scheme along with fractional calculus.
Qayyum Mubashir +5 more
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On Λ-Fractional Viscoelastic Models
Axioms, 2021 Λ-Fractional Derivative (Λ-FD) is a new groundbreaking Fractional Derivative (FD) introduced recently in mechanics. This derivative, along with Λ-Transform (Λ-T), provides a reliable alternative to fractional differential equations’ current solving.
Anastassios K. Lazopoulos +1 more
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