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Analytical study of atmospheric internal waves model with fractional approach

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Journal of Ocean Engineering and Science 2024年第4期9卷 326-337页

作者： Trushit Patel Hardik Patel ramakanta meher Computer Science University of the PeoplePasadenaCA 91101United States Department of Mathematics Uka Tarsadia UniversityBardoliGujaratIndia Mathematics and Humanities Department Sardar Vallabhbhai National Institute of TechnologySuratGujaratIndia

This study looks at the mathematical model of internal atmospheric waves,often known as gravity waves,occurring inside a fluid rather than on the *** the shallow-fluid assumption,internal atmospheric waves may be described by a nonlinear partial differential equation *** shallow flow model’s primary concept is that the waves are spread out across a large horizontal area before rising *** Fractional Reduced Differential Transform Method(FRDTM)is applied to provide approximate solutions for any given *** aids in the modelling of the global atmosphere,which has applications in weather and climate *** the integer-order value(α=1),the FRDTM solution is compared to the precise solution,EADM,and HAM to assess the correctness and efficacy of the proposed technique.

关键词： Shallow-fluid equations Atmospheric internal waves Time-fractional partial differential equations Fractional reduced differential transform method(FRDTM) Climate prediction

Numerical investigation on MHD Jeffery-Hamel nanofluid flow with different nanoparticles using fuzzy extension of generalized dual parametric homotopy algorithm

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Journal of Central South University 2024年第6期31卷 1915-1930页

作者： LALCHAND Verma ramakanta meher Department of Mathematics Sardar Vallabhbhai National Institute of TechnologySurat-395007GujratIndia

This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual parametric homotopy *** nanofluids have been formulated to enhance the thermophysical characteristics of fluids,including thermal diffusivity,conductivity,convective heat transfer coefficients and *** to the presence of distinct nanofluids,a change in the value of volume fraction occurs that influences the velocity profiles of the *** short value of nanoparticles volume fraction is considered an uncertain parameter and represented in a triangular fuzzy number range among[0.0,0.1,0.2].A novel generalized dual parametric homotopy algorithm with fuzzy extension is used here to study the fuzzy velocities at various channel ***,the effectiveness of the proposed approach has been demonstrated through a comparison with the available results in the crisp case.

关键词： fuzzy number Jeffery-Hamel(J-H)flow nanofluid homotopy analysis method

A robust fuzzy-fractional approach for the atmospheric internal wave model

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Journal of Ocean Engineering and Science 2023年第3期8卷 308-322页

作者： Parthkumar P.Sartanpara ramakanta meher Department of Mathematics and Humanities Sardar Vallabhbhai National Institute of TechnologySuratGujarat 395007India

The study of internal atmospheric waves,also known as gravity waves,which are detectable inside the fluid rather than at the fluid surface,is presented in this *** have used the time-fractional and fuzzy-fractional techniques to solve the differential equation system representing the atmospheric inter-nal waves *** q-Homotopy analysis Shehu transform technique(q-HAShTM)is used to solve the *** method helps find convergent solutions since it helps solve nonlinearity,and the fractional derivative can be easily computed using the Shehu ***,the obtained solution is compared for the particular case ofα=1 with the HAM solution to explain the method’s accuracy.

关键词： Atmospheric internal wave Fractional differential equation Fuzzy-fractional differential equation q-Homotopy analysis Shehu transform method

A robust computational approach for Zakharov-Kuznetsov equations of ion-acoustic waves in a magnetized plasma via the Shehu transform

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Journal of Ocean Engineering and Science 2023年第1期8卷 79-90页

作者： Parthkumar P.Sartanpara ramakanta meher Department of Mathematics and Humanities Sardar Vallabhbhai National Institute of TechnologySuratGujarat395007 India

The application of the q-homotopy analysis Shehu transform method(q-HAShTM)to discover the esti-mated solution of fractional Zakharov-Kuznetsov equations is investigated in this *** the presence of a uniform magnetic field,the Zakharov-Kuznetsov equations regulate the behaviour of nonlinear acoustic waves in a plasma containing cold ions and hot isothermal *** q-HAShTM is a stable analytical method that combines homotopy analysis and the Shehu *** q-homotopy investigation Shehu transform is a constructive method that leads to the Zakharov-Kuznetsov equations,which regulate the propagation of nonlinear ion-acoustic waves in a *** is a more semi-analytical method for adjust-ing and controlling the convergence region of the series solution and overcoming some of the homotopy analysis method’s limitations.

关键词： Zakharov-Kuznetsov equations q-Homotopy analysis Shehu transform method Shehu transform Caputo fractional derivatives

Fuzzy computational study on the generalized fractional smoking model with caputo gH-type derivatives

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International Journal of Biomathematics 2024年第4期17卷 151-194页

作者： Lalchand Verma ramakanta mehert Department of Mathematics&Humanities S.V.National Institute of Technology Surat-395007India

This work considers a generalized fuzzy fractional smoking model with Caputo gHtypes fractional derivatives upon considering the case of uncertainty *** disease-free equilibrium point and stability of the equilibrium point have been discussed for the fuzzy nonlinear fractional smoking *** analytical proofs for the existence and uniqueness of the proposed model are concerned with the help of the fixed-point theorem,Banach contraction,and Schauder theorem.A robust double parametric approach with a generalized transform is used to study the behavior of the fuzzy fractional model in an uncertain context and obtain the convergence analysis of the study in a crisp ***,the obtained results of the proposed model have been validated with the Runge-Kutta method of fourth order in crisp case(s=1,l=O).

关键词： Caputo fractional derivative triangular fuzzy number smoking model q-HAShTM convergence analysis

Study on effect of TiB2 reinforcement on the microstructural and mechanical properties of magnesium RZ5 alloy based metal matrix composites

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Journal of Magnesium and Alloys 2020年第3期8卷 780-792页

作者： Arabinda meher Manas Mohan Mahapatra Priyaranjan Samal Pandu R.Vundavilli School of Mechanical Sciences Indian Institute of Technology BhubaneswarOdisha 752050India

A self-propagating high-temperature synthesis route is adopted for the fabrication of TiB2-reinforced magnesium RZ5 alloy-based in-situ metal matrix ***-B is used according to the appropriate stoichiometry to obtain 4,6 and 8 wt.%TiB2 *** base alloy and cast composites are solutionised to enhance the mechanical properties of the materials.A microstructural study of the composites is carried out using optical microscopy and field emission seanning electron microscopy(FESEM)and revealed near-uniform distribution of TiB2 particles in the magnesium RZ5 alloy matrix.X-ray diffraction revealed the formation of the TiB2 reinforcement along with the transient phase TiB and *** hardness of the RZ5 alloy-based composites increases by 7.12%,17.06%and 32.07%with the addition of 4,6 and 8 wt.%TiB2 reinforcements,*** ultimate tensile strength of the as-cast composite increases by 30.47%with the addition of 8 wt.%*** tensile strength and ductility of the materials is improved by using the solutionising heat *** heat-treated composite containing 8 wt.%TiB2 results in an ultimate tensile strength of 178.7 *** tensile fracture surfaces are analysed using *** wear loss of the materials decreased from 25.826 mm^(3)to 22.949 mm^(3)by the adding 8 wt.%TiB2 for the sliding distance of 2000 *** of the worn surfaces obtained from FESEM of both the base alloy and composites are also studied which indicate delamination,wear groove and oxide formation.

关键词： In-situ composites Magnesium RZ5 alloy Heat-treatment Tensile strength Wear resistance.

A young man presenting with persistent hypoglycaemia and reduced level of consciousness: case study with review of literature

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World Journal of Emergency Medicine 2022年第5期13卷 418-421页

作者： meher Khan Nadia Kathrada Dean Nash Debkumar Chowdhury Critical Care Unit Royal Blackburn HospitalBlackburnBB23HHUnited Kingdom

Dear editor,Iatrogenic hypoglycaemia is a common acute presentation;either because of misuse,self-harm or criminal *** most common culprits are insulin and oral hypoglycaemics(sulfonylurea,biguanides)although aspirin,fluoroquinolone and beta blockers can be causative *** symptoms include sweating,anxiety,tremors,and *** symptoms usually arise at serum glucose concentrations of<2.8 mmol/L and include dizziness,confusion,blurred vision,somnolence and more serious symptoms can be convulsions,coma and potentially death.

关键词： acute editor tremor

Time-series analysis of monthly rainfall data for the Mahanadi River Basin, India

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Research in Cold and Arid Regions 2013年第1期5卷 73-84页

作者： Janhabi meher Ramakar Jha Department of Civil Engineering National Institute of Technology (NIT Rourkela) Orissa India

Time series analysis has two goals, modeling random mechanisms and predicting future series using historical data. In the present work, a uni-variate time series autoregressive integrated moving average （ARIMA） model has been developed for （a） simulating and forecasting mean rainfall, obtained using Theissen weights; over the Mahanadi River Basin in India, and （b） simula^ag and forecasting mean rainfall at 38 rain-gauge stations in district towns across the basin. For the analysis, monthly rainfall data of each district town for the years 1901-2002 （102 years） were used. Theissen weights were obtained over the basin and mean monthly rainfall was estimated. The trend and seasonality observed in ACF and PACF plots of rainfall data were removed using power transformation （a=0.5） and first order seasonal differencing prior to the development of the ARIMA model. Interestingly, the AR1MA model （1,0,0）（0,1,1）12 developed here was found to be most suitable for simulating and forecasting mean rainfall over the Mahanadi River Basin and for all 38 district town rain-gauge stations, separately. The Akaike Information Criterion （AIC）, good- ness of fit （Chi-square）, R2 （coefficient of determination）, MSE （mean square error） and MAE （mea absolute error） were used to test the validity and applicability of the developed ARIMA model at different stages. This model is considered appropriate to forecast the monthly rainfall for the upcoming 12 years in each district town to assist decision makers and policy makers establish priorities for water demand, storage, distribution, and disaster management.

关键词： Akaike Information Criterion autoregressive integrated moving average model goodness of fit rainfall forecasting

Numerical treatment of temporal-fractional porous medium model occurring in fractured media

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Journal of Ocean Engineering and Science 2023年第5期8卷 481-499页

作者： R.meher J.Kesarwani Z.Avazzadeh O.Nikan Department of Applied Mathematics&Humanities S.V.National Institute of TechnologySurat 395007India Department of Applied Mathematics Xi’an Jiaotong-Liverpool UniversitySuzhou 215123China School of Mathematics Iran University of Science and TechnologyNarmakTehran 16846-13114Iran

This paper proposes a temporal-fractional porous medium model(T-FPMM)for describing the co-current and counter-current imbibition,which arises in a water-wet fractured porous *** correlation be-tween the co-current and counter-current imbibition for the fractures and porous matrix are examined to determine the saturation and recovery rate of the *** different fractional orders in both porous matrix and fractured porous media,the homotopy analysis technique and its stability analysis are used to explore the parametric behavior of the saturation and recovery ***,the effects of wettability and inclination on the recovery rate and saturation are studied for distinct fractional values.

关键词： Fractured porous media Caputo fractional derivative Co-current imbibition Time-fractional partial differential equation