Reproducing kernel Hilbert space method based on reproducing kernel functions for investigating boundary layer flow of a Powell–Eyring non-Newtonian fluid

Akgül, Ali

doi:10.1080/16583655.2019.1651988

Cited by 42 publications

(17 citation statements)

References 30 publications

(36 reference statements)

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“…As soon as a person is infected, the proportion of becoming in I is

, which means that the proportion of becoming in Q equal

[28] . There are a number of numerical methods that are used to solve fractional differential equations such as those in [29] , [30] , [31] , [32] . We use Laplace transform technique to solve the model as follows:…”

Section: Model Formulationmentioning

confidence: 99%

Fractional mathematical modeling for epidemic prediction of COVID-19 in Egypt

Sherief

2021

Ain Shams Engineering Journal

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In this work the concept of fractional derivative is used to improve a mathematical model for the spread of the novel strain of corona virus disease COVID-19 in Egypt. We establish the dynamics model to predict the transmission of COVID-19. The results predicted by the model show a good agreement with the actual reported data. The effect of precautionary measures on the behavior of the model was studied and it was confirmed that the quarantine period should be long enough to achieve the desired result.

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“…As soon as a person is infected, the proportion of becoming in I is

, which means that the proportion of becoming in Q equal

Section: Model Formulationmentioning

confidence: 99%

Fractional mathematical modeling for epidemic prediction of COVID-19 in Egypt

Sherief

2021

Ain Shams Engineering Journal

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“…Based on the RKFs theory [10], a class of numerical approaches to solve differential and integral equations were developed and improved (see, e.g., [1–5, 7, 8, 23–27, 30, 33, 34, 36, 39, 40]). In order to solve (2.2) on the basis of the RKFs theory, we shall introduce the approximation in the RKHS and the Mittag‐Leffler RKFs for estimating Caputo time fractional derivative.…”

Section: Numerical Approachmentioning

confidence: 99%

Kernel functions‐based approach for distributed order diffusion equations

Geng

2020

Numerical Methods Partial

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In this work, we solve distributed order diffusion equations (DODEs) by applying the theory on reproducing kernel functions (RKFs). The classical numerical quadrature formulae is used to approximate the DODE to a multi‐term Caputo fractional order diffusion equation (FDE). The Mittag‐Leffler RKF is introduced to estimate fractional derivatives of Caputo. And a space–time RKFs collocation scheme is derived for the multi‐term Caputo time FDEs. The accuracy of the present numerical technique is indicated by employing several experiments.

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“…Besides calculating the time-evolution of the wave function and the way to minimize the cost function we used as described in ref. [30], there are other mathematical ways about fractional derivatives to calculate differential equations [36][37][38][39][40][41][42][43][44][45]. Figure 3(a) shows the atomic wave function as time when the dimple-ring potential is shaken, resulting in the optimized control to excite the ground state of the dimplering trap for 20 ms and hold the excited state in the dimplering trap for 20 ms. Figure 3(b) shows the optimized control in black and the initial guess in red.…”

Section: ∫ ( ( )mentioning

confidence: 99%

Optimal control for generating excited state expansion in ring potential

Kim

2020

Open Physics

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We applied an optimal control algorithm to an ultra-cold atomic system for constructing an atomic Sagnac interferometer in a ring trap. We constructed a ring potential on an atom chip by using an RF-dressed potential. A field gradient along the radial direction in a ring trap known as the dimple-ring trap is generated by using an additional RF field. The position of the dimple is moved by changing the phase of the RF field [1]. For Sagnac interferometers, we suggest transferring Bose–Einstein condensates to a dimple-ring trap and shaking the dimple potential to excite atoms to the vibrational-excited state of the dimple-ring potential. The optimal control theory is used to find a way to shake the dimple-ring trap for an excitation. After excitation, atoms are released from the dimple-ring trap to a ring trap by adiabatically turning off the additional RF field, and this constructs a Sagnac interferometer when opposite momentum components are overlapped. We also describe the simulation to construct the interferometer.

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Reproducing kernel Hilbert space method based on reproducing kernel functions for investigating boundary layer flow of a Powell–Eyring non-Newtonian fluid

Cited by 42 publications

References 30 publications

Fractional mathematical modeling for epidemic prediction of COVID-19 in Egypt

Fractional mathematical modeling for epidemic prediction of COVID-19 in Egypt

Kernel functions‐based approach for distributed order diffusion equations

Optimal control for generating excited state expansion in ring potential

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