Analytical method to solve the local fractional vehicular traffic flow model

Singh, Nisha; Kumar, Kranti; Goswami, Pranay; Jafari, Hossein

doi:10.1002/mma.8027

Cited by 15 publications

(7 citation statements)

References 27 publications

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“…In numerous studies, the local fractional derivative/integral was used for representing most engineering and physical processes, which in some situations provides an appropriate description of these models in a comparison of integer-order derivatives. As a result, the use of fractional calculus is the right choice for explaining the real world (Xiao-Jun et al , 2017; Hemeda et al , 2018; Baleanu et al , 2019; Jassim, 2020; Singh et al , 2022; Aly et al , 2022).…”

Section: Introductionmentioning

confidence: 99%

Natural convection of NEPCM in a partial porous H-shaped cavity: ISPH simulation

Aly

Alsedais

2023

HFF

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Purpose This paper aims to investigate the conformable fractal approaches of unsteady natural convection in a partial layer porous H-shaped cavity suspended by nano-encapsulated phase change material (NEPCM) by the incompressible smoothed particle hydrodynamics method. Design/methodology/approach The partial hot sources with variable height L_Hot are in the H-cavity’s sides and center. The performed numerical simulations are obtained at the variations of the following parameters: source of hot length L_Hot = (0.4–1.6), conformable fractal parameter α (0.97–1), fusion temperature θf (0.05–0.9), thermal radiation parameter Rd (0–7), Rayleigh number Ra (103–106), Darcy parameter Da (10−2 to 10−5) and Hartmann number Ha (0–80). Findings The main outcomes showed the implication of hot source length L_Hot, Rayleigh number and fusion temperature in controlling the contours of a heat capacity within H-shaped cavity. The presence of a porous layer in the right zone of H-shaped cavity prevents the nanofluid flow within this area at lower Darcy parameter. An increment in the thermal radiation parameter declines the heat transfer and changes the heat capacity contours within H-shaped cavity. The velocity field is strongly enhanced by an augmentation on Rayleigh number. Increasing the Hartmann number shrinks the velocity field within H-shaped cavity. Originality/value The novelty of this work is solving the conformable fractal approaches of unsteady natural convection in a partial layer porous H-shaped cavity suspended by NEPCM.

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Section: Introductionmentioning

confidence: 99%

Natural convection of NEPCM in a partial porous H-shaped cavity: ISPH simulation

Aly

Alsedais

2023

HFF

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“…The LWR model offers a further static relationship between density and flow in the traffic stream. Moreover, because it only requires a small number of model variables, this model is also used for large-scale simulations [5,6,7,8,9]. A numerical technique was recently used by Tower et al [10] to study discontinuous velocity version of LWR model.…”

Section: Introductionmentioning

confidence: 99%

“…Local fractional calculus currently seems a constructive field of applied mathematics in order to investigate the characteristics of fractal space-based physical models. It has been effectively used in several domains, including physics, signal processing, quantum mechanics, fluid dynamics, applied mathematics, and others, to tackle fractal problems [1,5]. As a result, this new approach to fractional calculus has been applied by a large number of researchers to the simulation of natural phenomena.. Babakhani and Gejji [12] conducted extensive research on the local fractional derivative, and Yang [13,14] further developed and refined their findings.…”

Section: Introductionmentioning

confidence: 99%

A Generalized Local Fractional LWR Model of Vehicular Traffic Flow and Its Solution

Goswami

Pokhriyal

2023

Preprint

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In this study, a generalized nonlinear local fractional Lighthill-Whitham-Richards (LFLWR) model has been developed. The local fractional variational iteration method (LFVIM) solves and analyzes the proposed model. Numerous works have been described in past to address linear LWR and linear LFLWR models. This research highlighted on generalized nonlinear LFLWR model and LFVIM is employed to derive non-differentiable solutions of the suggested model. The existence and uniqueness of the resolution of LFLWR model have also been established. Furthermore, several exemplary instances are discussed to demonstrate the success of implementing LFVIM to the proposed model. The numerical simulations for each of the cases have also been shown. Additionally, the obtained solutions of the suggested model have been compared with the solutions of the classical LWR model with non-differentiable conditions in few examples. The study demonstrates that the employed iterative scheme is quite efficient and can be utilized for obtaining the non-differentiable solution to proposed generalized nonlinear LFLWR model of traffic flow.

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“…The LWR model offers a further static relationship between density and flow in the traffic stream. Moreover, because it only requires a small number of model variables, this model is also used for large-scale simulations [7][8][9][10][11]. A numerical technique was recently used by Tower et al [12] to study discontinuous velocity version of LWR model.…”

Section: Introductionmentioning

confidence: 99%

A generalized local fractional LWR model of vehicular traffic flow and its solution

Pokhriyal

Goswami

2023

Math Methods in App Sciences

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In this study, a generalized nonlinear local fractional Lighthill‐Whitham‐Richards (LFLWR) model has been developed. The local fractional variational iteration method (LFVIM) solves and analyzes the proposed model. Numerous works have been described in the past to address linear LWR and linear LFLWR models. This research highlighted on generalized nonlinear LFLWR model, and LFVIM is employed to derive non‐differentiable solutions of the suggested model. The existence and uniqueness of the solution of LFLWR model have also been established. Furthermore, several exemplary instances are discussed to demonstrate the success of implementing LFVIM to the proposed model. The numerical simulations for each of the cases have also been shown. Additionally, the obtained solutions of the suggested model have been compared with the solutions of the classical LWR model with non‐differentiable conditions in few examples. The study demonstrates that the employed iterative scheme is quite efficient and can be utilized to obtain the non‐differentiable solution to the proposed generalized nonlinear LFLWR traffic flow model.

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Analytical method to solve the local fractional vehicular traffic flow model

Cited by 15 publications

References 27 publications

Natural convection of NEPCM in a partial porous H-shaped cavity: ISPH simulation

Natural convection of NEPCM in a partial porous H-shaped cavity: ISPH simulation

A Generalized Local Fractional LWR Model of Vehicular Traffic Flow and Its Solution

A generalized local fractional LWR model of vehicular traffic flow and its solution

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