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An Efficient Computational Technique for Fractal Vehicular Traffic Flow.

Devendra Kumar1, Fairouz Tchier2, Jagdev Singh1

  • 1Department of Mathematics, JECRC University, Jaipur 303905, India.

Entropy (Basel, Switzerland)
|December 3, 2020
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Summary

This study solves complex fractal vehicular traffic flow problems using advanced mathematical techniques. The methods efficiently provide non-differentiable solutions, enhancing traffic flow analysis.

Keywords:
fractal vehicular traffic flowhomotopy perturbation techniquelocal fractional Sumudu transformlocal fractional derivativereduced differential transform method

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Area of Science:

  • Mathematical modeling
  • Applied mathematics
  • Traffic flow dynamics

Background:

  • Vehicular traffic flow is often modeled using partial differential equations.
  • Fractal dynamics introduce complexities not captured by traditional models.
  • Non-differentiable solutions are crucial for understanding real-world traffic phenomena.

Purpose of the Study:

  • To solve partial differential equations for fractal vehicular traffic flow.
  • To apply and validate novel analytical techniques for complex traffic systems.
  • To obtain non-differentiable solutions for fractal traffic models.

Main Methods:

  • Local fractional homotopy perturbation Sumudu transform scheme
  • Local fractional reduced differential transform method
  • Solving fractal partial differential equations

Main Results:

  • Demonstrated the effectiveness of the proposed analytical techniques.
  • Successfully obtained non-differentiable solutions for fractal traffic flow.
  • Illustrative examples confirmed the accuracy and efficiency of the methods.

Conclusions:

  • The presented schemes are highly efficient for fractal vehicular traffic flow problems.
  • These methods provide a robust framework for analyzing complex, non-differentiable traffic dynamics.
  • The study highlights the utility of advanced mathematical tools in transportation science.