An approximate analytical solution of the time-fractional Navier–Stokes equations by the generalized Laplace residual power series method

Dunnimit, P.; Sawangtong, W.; Sawangtong, P.

doi:10.1016/j.padiff.2024.100629

Cited by 5 publications

(1 citation statement)

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“…The Caputo FD model, which has a singular power law kernel, is the most appropriate fractional operator to be used in modeling real world problems. In fact, it has been widely used in many scientific disciplines such as anomalous diffusion [8], fluid mechanics [9], porous media [10], signal processing [11], viscoelastic materials [12], optimal control [13], electrical networks [14], electromagnetism [15], heat transfer [16], biology [17] and other disciplines [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

On a fractional derivative operator with a singular kernel: definition, properties and numerical simulation

Odibat

2024

Phys. Scr.

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This paper is concerned with proposing a novel nonlocal fractional derivative operator with a singular kernel. We considered a fractional integral operator as a single integral of convolution type combined with a Mittag-Leffler kernel of Prabhakar type. The proposed singular fractional derivative operator is formulated as a proper inverse of the considered integral operator. We provided some useful features and relationships of the proposed derivative and introduced comparisons with the Caputo derivative which can be utilized for potential applications. Next, we presented numerical solutions for some nonlinear fractional order models incorporating the proposed derivative using a numerical algorithm developed in this paper. As a case study, we discussed the dynamic behavior of a fractional logistic model with the proposed derivative.

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