Applications of New Time and Spatial Fractional Derivatives with Exponential Kernels

Caputo, Michèle; Fabrizio, Mauro

doi:10.18576/pfda/020101

Cited by 663 publications

(569 citation statements)

References 5 publications

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“…However, there were some serious issues that were pointed out against this new finding. First the kernel used was not non-local; second the anti-derivative associated is just the average of the function and its integral [1,2,4,[8][9][10][11]. Therefore it was concluded that, the operator was rather a filter than a fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Atangana-Baleanu derivative with fractional order applied to the model of groundwater within an unconfined aquifer

Alqahtani¹

2016

J. Nonlinear Sci. Appl.

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The power law has been used to construct the derivative with fractional order in Caputo and RiemannLiouville sense, if we viewed them as a convolution. However, it is not always possible to find the power law behaviour in nature. In 2016 Abdon Atangana and Dumitru Baleanu proposed a derivative that is based upon the generalized Mittag-Leffler function, since the Mittag-Leffler function is more suitable in expressing nature than power function. In this paper, we applied their new finding to the model of groundwater flowing within an unconfined aquifer.

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Section: Introductionmentioning

confidence: 99%

Atangana-Baleanu derivative with fractional order applied to the model of groundwater within an unconfined aquifer

Alqahtani¹

2016

J. Nonlinear Sci. Appl.

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“…The relationship between flap angle and azimuth angle, with different collective pitch θ 0 under conditions of θ 1c = 4 ∘ , θ 1s = −0 ∘ , and µ = 0.4, was obtained by solving the flap equation using the boundary value combined with the Snel stall model and B-L model (BeddoesLeishman) [21,22], as shown in Fig. 4.…”

Section: Validating the Snel Stall Modelmentioning

confidence: 99%

Flap motion of helicopter rotors with novel, dynamic stall model

Wang

Liu

Liu³

et al. 2016

Open Physics

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Abstract:In this paper, a nonlinear flapping equation for large inflow angles and flap angles is established by analyzing the aerodynamics of helicopter blade elements. In order to obtain a generalized flap equation, the Snel stall model was first applied to determine the lift coefficient of the helicopter rotor. A simulation experiment for specific airfoils was then conducted to verify the effectiveness of the Snel stall model as it applies to helicopters. Results show that the model requires no extraneous parameters compared to the traditional stall model and is highly accurate and practically applicable. Based on the model, the relationship between the flapping angle and the angle of attack was analyzed, as well as the advance ratio under the dynamic stall state.

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“…In 2015, a new fractional derivation without singular kernel was introduced by Caputo and Fabrizio ( [8]). Some researchers tried to use it for solving different equations (see, for example, [2,9] and [14]). Recently, approximate solutions of some fractional differential equations have been reviewed (see, for example, [3,4,6,12,13] and [7]).…”

Section: Introductionmentioning

confidence: 99%

On high order fractional integro-differential equations including the Caputo–Fabrizio derivative

et al. 2018

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Applications of New Time and Spatial Fractional Derivatives with Exponential Kernels

Cited by 663 publications

References 5 publications

Atangana-Baleanu derivative with fractional order applied to the model of groundwater within an unconfined aquifer

Atangana-Baleanu derivative with fractional order applied to the model of groundwater within an unconfined aquifer

Flap motion of helicopter rotors with novel, dynamic stall model

On high order fractional integro-differential equations including the Caputo–Fabrizio derivative

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