An efficient computational technique for time‐fractional<scp>Kaup‐Kupershmidt</scp>equation

Prakasha, D. G.; Malagi, Naveen Sanju; Veeresha, P.; Prasannakumara, B. C.

doi:10.1002/num.22580

Cited by 27 publications

(8 citation statements)

References 45 publications

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“…A good number of exact, analytical, and numerical Schemes [53][54][55][56] are available in the literature. For the system of Equations ( 7)-( 9) the numerical scheme of MATLAB bvp4c is applied.…”

Section: Numerical Schemementioning

confidence: 99%

Model‐based comparative study of magnetohydrodynamics unsteady hybrid nanofluid flow between two infinite parallel plates with particle shape effects

Chu

Bashir

Ramzan

et al. 2022

Math Methods in App Sciences

233

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The present study examines the impact of unsteady viscous flow in a squeezing channel. Silver–gold hybrid nanofluid particles with different shapes are inserted in the base fluid engine oil. Flow and heat transfer mechanism is detected in the presence of magnetohydrodynamics between the two parallel infinite plates. The thermal conductivity models, that is, Yamada–Ota and Hamilton–Crosser models are used to investigate various shapes (Blade, platelet, cylinder, and brick) of hybrid nanoparticles. The model is made up of paired high nonlinear partial differential equations that are then transformed into ordinary differential equations which are coupled and strong nonlinear using the boundary layer approximation. The MATLAB solver bvp4c package is used to solve the numerical solution of this coupled system. The influence of different parameters on the physical quantities is addressed via graphs. A comparison with already reported results is given in order to confirm the current findings. The analysis shows that surprisingly the Yamada–Ota model of the Hybrid nanofluid gains high temperature and velocity profile than the Hamilton–Crosser model of the hybrid nanofluid. Also, both the models show increasing trends toward increasing the volume fraction rate of silver‐gold hybrid nanoparticles. It is also inferred that the hybrid‐nanoparticles performance is far better than the common nanofluids.

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Section: Numerical Schemementioning

confidence: 99%

Model‐based comparative study of magnetohydrodynamics unsteady hybrid nanofluid flow between two infinite parallel plates with particle shape effects

Chu

Bashir

Ramzan

et al. 2022

Math Methods in App Sciences

233

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show abstract

“…Moreover, it is the generalization of many methods (results attained by this technique is a particular case for the value of parameters associated to method). The projected algorithm has been employed due to its efficiency and accuracy to examine the extensive classes of complex as well as nonlinear models and problems and also for the system of equations [60][61][62][63][64][65][66][67]. Recently, many interesting consequences are derived by using the projected scheme while analyzing the real-world problem.…”

Section: Introductionmentioning

confidence: 99%

A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators

Veeresha

Yavuz

Baishya

2021

Int. J. Optim. Control, Theor. Appl. (IJOCTA)

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The Korteweg–De Vries (KdV) equation has always provided a venue to study and generalizes diverse physical phenomena. The pivotal aim of the study is to analyze the behaviors of forced KdV equation describing the free surface critical flow over a hole by finding the solution with the help of q-homotopy analysis transform technique (q-HATT). he projected method is elegant amalgamations of q-homotopy analysis scheme and Laplace transform. Three fractional operators are hired in the present study to show their essence in generalizing the models associated with power-law distribution, kernel singular, non-local and non-singular. The fixed-point theorem employed to present the existence and uniqueness for the hired arbitrary-order model and convergence for the solution is derived with Banach space. The projected scheme springs the series solution rapidly towards convergence and it can guarantee the convergence associated with the homotopy parameter. Moreover, for diverse fractional order the physical nature have been captured in plots. The achieved consequences illuminates, the hired solution procedure is reliable and highly methodical in investigating the behaviours of the nonlinear models of both integer and fractional order.

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“…Musette introduced the fifth-order KK equation, and Verhoeven was one of the combined instances of the Henon-Heiles method; see [17] for more details. Prakasha et al [18] used the q-homotopy analysis transform method which is implemented to obtain the result for the fractionalorder KK equation.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Fractional-Order Kaup–Kupershmidt Equation via Novel Transforms

Iqbal

Yasmin

Rezaiguia

et al. 2021

Journal of Mathematics

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In this article, we develop a technique to determine the analytical result of some Kaup–Kupershmidt equations with the aid of a modified technique called the new iteration transform method. This technique is a mixture of the novel integral transformation Elzaki transformation and the new iteration technique. The nonlinear term can be handled easily by a new iteration technique. The results show that the combination of the Elzaki transformation and the new iteration technique is quite capable and basically well suited for applying in such problems and that it can be implemented to other nonlinear models. This technique is viewed as an effective alternative approach to certain existing approaches for such accurate models.

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An efficient computational technique for time‐fractionalKaup‐Kupershmidtequation

Cited by 27 publications

References 45 publications

Model‐based comparative study of magnetohydrodynamics unsteady hybrid nanofluid flow between two infinite parallel plates with particle shape effects

Model‐based comparative study of magnetohydrodynamics unsteady hybrid nanofluid flow between two infinite parallel plates with particle shape effects

A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators

Analysis of the Fractional-Order Kaup–Kupershmidt Equation via Novel Transforms

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