Splines solutions of boundary value problems that arises in sculpturing electrical process of motors with two rotating mechanism circuit

A fractal-fractional-order modified Predator-Prey mathematical model with immigrations

In this study we propose a fractional frequency flexible Fourier form fractionally integrated ADF unit-root test, which combines the fractional integration and nonlinear trend as a form of the Fourier function. We provide the asymptotics of the newly proposed test and investigate its small-sample properties. Moreover, we show the best estimators for both fractional frequency and fractional difference operator for our newly proposed test. Finally, an empirical study demonstrates that not considering the structural break and fractional integration simultaneously in the testing process may lead to misleading results about the stochastic behavior of the Covid-19 pandemic.

/pdf/fractional-unit-root-tests-allowing-for-a-fractional-53rxo97656.pdf

Fractional unit-root tests allowing for a fractional frequency flexible Fourier form trend: predictability of Covid-19

Fluids like hybrid nanofluids have great potential that present exceptional thermal behavior and thermophysical properties as compare to ordinary nanofluids. Hybrid nanofluids are obtained by the mixture of two different nanoparticles in a base fluid. Many scholars stated that hybrid-nanofluids could be replaced by conventional coolants, especially fluids which work at high temperature. Therefore, these kinds of nanofluids are less damaging for environmental impact and also lead to save energy. The main idea of hybrid nanofluids is to develop performance of heat transfer and its advantages has directed to comparatively good hope for its applications. The objective of present article is to examine 3D stagnation point flow of hybrid nanofluid passes along a stretchable heated wavy cylinder under the impact of variable thickness and slip conditions. For this purpose we consider alloy particles of AA7075 + AA7072 and AA7072 which are suspended in methanol liquid. The alloy particles merged in this analysis are entirely manufactured materials as well as possessing higher heat transfer characteristics. Alloy AA7072 is a combination of zinc and aluminum in ratio 1:98 with addition of metals like silicon, copper and ferrous. Similarly, alloy AA7075 is a combination of zinc, aluminum, copper and magnesium in ratio −6, −9, −1 and −3 respectively with addition of metals like silicon, magnesium and ferrous. The scenario of this model is scrutinized mathematically by captivating induced magnetic field with in the domain of thermal boundary layer. Similarity transformations are deployed to change the governing equations into nonlinear ODEs and consequently solved this system through bvp4c solver. The impact of emerging parameters on velocity, induction and energy distributions are examined through graphical depiction. Furthermore, heat transfer rates and drag forces near the boundary are designed numerically in tabular form.

A hybrid nanofluid flow near a highly magnetized heated wavy cylinder

Fluids like hybrid nanofluids have great potential that present exceptional thermal behavior and thermophysical properties as compare to ordinary nanofluids. Hybrid nanofluids are obtained by the mixture of two different nanoparticles in a base fluid. Many scholars stated that hybrid-nanofluids could be replaced by conventional coolants, especially fluids which work at high temperature. Therefore, these kinds of nanofluids are less damaging for environmental impact and also lead to save energy. The main idea of hybrid nanofluids is to develop performance of heat transfer and its advantages has directed to comparatively good hope for its applications. The objective of present article is to examine 3D stagnation point flow of hybrid nanofluid passes along a stretchable heated wavy cylinder under the impact of variable thickness and slip conditions. For this purpose we consider alloy particles of AA7075 + AA7072 and AA7072 which are suspended in methanol liquid. The alloy particles merged in this analysis are entirely manufactured materials as well as possessing higher heat transfer characteristics. Alloy AA7072 is a combination of zinc and aluminum in ratio 1:98 with addition of metals like silicon, copper and ferrous. Similarly, alloy AA7075 is a combination of zinc, aluminum, copper and magnesium in ratio −6, −9, −1 and −3 respectively with addition of metals like silicon, magnesium and ferrous. The scenario of this model is scrutinized mathematically by captivating induced magnetic field with in the domain of thermal boundary layer. Similarity transformations are deployed to change the governing equations into nonlinear ODEs and consequently solved this system through bvp4c solver. The impact of emerging parameters on velocity, induction and energy distributions are examined through graphical depiction. Furthermore, heat transfer rates and drag forces near the boundary are designed numerically in tabular form. 

In this work, we have developed a numerical algorithm based on redefined extended cubic B-spline functions to explore the approximate solution for time fractional Klein--Gorden equation. The presented technique engages finite difference formulation for discretizing the Caputo time fractional derivative of order $\alpha \in (1,2]$ and redefined extended cubic B-spline functions to interpolate the solution curve along spatial grid. A stability analysis of the scheme is set up to affirm that the errors do not amplify during the execution of numerical procedure. The derivation of uniform convergence reveals that the scheme is $O(h^{2}+\Delta t^{2-\alpha})$ accurate. Some computational experiments are carried out to verify the theoretical considerations. Numerical results are compared with the existing techniques on the topic and it is concluded that the present scheme returns superior outcomes.

/pdf/numerical-treatment-of-time-fractional-klein-gordon-equation-18oujohwkn.pdf

Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions

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Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions