The Analysis of the Fractional-Order Navier-Stokes Equations by a Novel Approach

Elsayed, E. M.; Shah, Rasool; Nonlaopon, Kamsing

doi:10.1155/2022/8979447

Cited by 26 publications

(8 citation statements)

References 49 publications

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“…Fractional calculus is widely used to improve existing mathematical models due to its special ability to explain irregular behavior and memory affects, which are the key components of complex phenomena (Caputo 1969, Caputo 2015. Due to its numerous applications in a wide range of non-linear complex systems occurring physics, life sciences, mathematical biology, viscoelasticity, fluid mechanics, electrochemistry, fractional calculus is becoming more and more popular every day (Elsayed 2022). Non-linear problems are significant to engineers, physicists, and mathematicians because most of the physical systems in nature are nonlinear (Hajira 2020).…”

Section: Introductionmentioning

confidence: 99%

A semi-analytical approach via yang transform on fractional-order navier-stokes equation

Kapoor,

Kour

2023

Phys. Scr.

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In this current, the applications of the Yang transformation technique are taken under consideration to deal with the non-linear fractional Navier–Stokes equation and fractional coupled Navier–Stokes equation. The suggested method produces approximate-analytical solutions in the form of a series that are correspondingly dependent on fractional-order derivative values and have modest, comprehensible mechanics and easy implementation. The Caputo fractional derivative is employed, and the numerical scheme’s stability and convergence are examined. Numerical examples demonstrate the analytical solution of the technique and it is examined that the proposed techniques are robust, efficient and reduce the number of numerical computations. The current technique’s results are compatible with the theoretical analysis, and the suggested technique can be extended to solve numerous higher-order non-linear dynamics.

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Section: Introductionmentioning

confidence: 99%

A semi-analytical approach via yang transform on fractional-order navier-stokes equation

Kapoor,

Kour

2023

Phys. Scr.

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“…In the nineteenth century, systematic classifications of planar and spatial patterns emerged. Solving fractional nonlinear differential equations with precision has proven to be rather challenging [29,35,36].…”

Section: Introductionmentioning

confidence: 99%

Fractional View Analysis of Kuramoto–Sivashinsky Equations with Non-Singular Kernel Operators

et al. 2022

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In this article, we investigate the nonlinear model describing the various physical and chemical phenomena named the Kuramoto–Sivashinsky equation. We implemented the natural decomposition method, a novel technique, mixed with the Caputo–Fabrizio (CF) and Atangana–Baleanu deriavatives in Caputo manner (ABC) fractional derivatives for obtaining the approximate analytical solution of the fractional Kuramoto–Sivashinsky equation (FKS). The proposed method gives a series form solution which converges quickly towards the exact solution. To show the accuracy of the proposed method, we examine three different cases. We presented proposed method results by means of graphs and tables to ensure proposed method validity. Further, the behavior of the achieved results for the fractional order is also presented. The results we obtain by implementing the proposed method shows that our technique is extremely efficient and simple to investigate the behaviour of nonlinear models found in science and technology.

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“…Fractional calculus has grown in popularity in recent decades, owing to its demonstrated applications in a variety of seemingly diverse and large-ranging fields of science and engineering, such as fluid flow, rheology, dynamical processes, porous structures, diffusive transport akin to diffusion, control theory of dynamical systems and viscoelasticity, etc., for example [18][19][20][21][22]. The models given by partial differential equations with fractional derivatives are the most important.…”

Section: Introductionmentioning

confidence: 99%

Local and Global Existence and Uniqueness of Solution for Time-Fractional Fuzzy Navier–Stokes Equations

et al. 2022

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Navier–Stokes (NS) equation, in fluid mechanics, is a partial differential equation that describes the flow of incompressible fluids. We study the fractional derivative by using fractional differential equation by using a mild solution. In this work, anomaly diffusion in fractal media is simulated using the Navier–Stokes equations (NSEs) with time-fractional derivatives of order β∈(0,1). In Hγ,℘, we prove the existence and uniqueness of local and global mild solutions by using fuzzy techniques. Meanwhile, we provide a local moderate solution in Banach space. We further show that classical solutions to such equations exist and are regular in Banach space.

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The Analysis of the Fractional-Order Navier-Stokes Equations by a Novel Approach

Cited by 26 publications

References 49 publications

A semi-analytical approach via yang transform on fractional-order navier-stokes equation

A semi-analytical approach via yang transform on fractional-order navier-stokes equation

Fractional View Analysis of Kuramoto–Sivashinsky Equations with Non-Singular Kernel Operators

Local and Global Existence and Uniqueness of Solution for Time-Fractional Fuzzy Navier–Stokes Equations

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