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Yıl 2017, Cilt: 7 Sayı: 1, 58 - 65, 01.06.2017

Öz

Kaynakça

  • Ansorge,R., (1990), What does the entropy condition mean in traffic flow theory, Transportation Research Part B, 24(2), pp.133-143.
  • Li,Y., Wang,L.F., Zeng,S D. and Zhao,Y., (2014), Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow, Advances in Mathematical Physics, 2014, pp.1-7.
  • Wang,L.F., Yang,X.J., Baleanu,D., Cattani,C. and Zhao,Y., (2014), Fractal Dynamical Model of Vehicular Traffic Flow within the Local Fractional Conservation Laws, 2014, pp.1-5.
  • Yang,X.J. and Baleanu,D., (2013), Fractal heat conduction problem solved by local fractional varia- tional iteration method, Thermal Science, 17(2), pp.625-628.
  • Xu,S., Ling,X., Zhao,Y. and Jassim,H.K., (2015), A Novel Schedule for Solving the Two-Dimensional Diffusion in Fractal Heat Transfer, Thermal Science, 19(1), pp.99-103.
  • Yang,A.M., Yang,X.J. and Li,Z.B., (2013), Local Fractional series expansion method for Solving wave and diffusion Equations on Cantor sets, Abstract and Applied Analysis, 2013, pp.1-6.
  • Jafari,H. and Jassim,H.K., (2015), Application of the Local fractional Adomian Decomposition and Series Expansion Methods for Solving Telegraph Equation on Cantor Sets Involving Local Fractional Derivative Operators, Journal of Zankoy Sulaimani-Part A, 17(2), pp.15-22.
  • Jafari,H. and Jassim,H.K., (2014), Local Fractional Adomian Decomposition Method for Solving Two Dimensional Heat conduction Equations within Local Fractional Operators, Journal of Advance in Mathematics, 9(4), pp.2574-2582.
  • Wang,S.Q., Yang,Y.J. and Jassim,H.K., (2014), Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative, Abstract and Applied Analysis, 2014, pp.1-7.
  • Yan,S.P., Jafari,H. and Jassim,H.K., (2014), Local Fractional Adomian Decomposition and Function Decomposition Methods for Solving Laplace Equation within Local Fractional Operators, Advances in Mathematical Physics, 2014, pp.1-7.
  • Jafari,H. and Jassim,H.K., (2014), Local Fractional Laplace Variational Iteration Method for Solving Nonlinear Partial Differential Equations on Cantor Sets within Local Fractional Operators, Journal of Zankoy Sulaimani-Part A, 16(4), pp.49-57.
  • Jassim, H. K., Unlu, C., Moshokoa, S. P. and Khalique, C. M., (2015), Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators, Mathematical Problems in Engineering, 2015, pp. 1-9.
  • Jafari,H. and Jassim,H.K., Moshokoa,S.P., Ariyan,V.M. and Tchier,F., (2016), Reduced differential transform method for partial differential equations within local fractional derivative operators, Ad- vances in Mechanical Engineering, 8(4), pp.1-6.
  • Jafari,H. and Jassim,H.K., (2015), Numerical Solutions of Telegraph and Laplace Equations on Cantor Sets Using Local Fractional Laplace Decomposition Method , International Journal of Advances in Applied Mathematics and Mechanics, 2(3), pp.144-151.

ON APPROXIMATE METHODS FOR FRACTAL VEHICULAR TRAFFIC FLOW

Yıl 2017, Cilt: 7 Sayı: 1, 58 - 65, 01.06.2017

Öz

In this paper, we find the approximate solutions for partial differential equations arising in fractal vehicular traffic flow by using the local fractional Laplace decomposition method LFLDM and local fractional series expansion method LFSEM . These methods provide us with a convenient way to find the approximate solution with less computation as compared with local fractional variational iteration method. The results obtained by the proposed methods LFLDM and LFSEM are compared with the results obtained by LFLVIM . Some examples are presented to illustrate the efficiency and accuracy of the proposed methods.

Kaynakça

  • Ansorge,R., (1990), What does the entropy condition mean in traffic flow theory, Transportation Research Part B, 24(2), pp.133-143.
  • Li,Y., Wang,L.F., Zeng,S D. and Zhao,Y., (2014), Local Fractional Laplace Variational Iteration Method for Fractal Vehicular Traffic Flow, Advances in Mathematical Physics, 2014, pp.1-7.
  • Wang,L.F., Yang,X.J., Baleanu,D., Cattani,C. and Zhao,Y., (2014), Fractal Dynamical Model of Vehicular Traffic Flow within the Local Fractional Conservation Laws, 2014, pp.1-5.
  • Yang,X.J. and Baleanu,D., (2013), Fractal heat conduction problem solved by local fractional varia- tional iteration method, Thermal Science, 17(2), pp.625-628.
  • Xu,S., Ling,X., Zhao,Y. and Jassim,H.K., (2015), A Novel Schedule for Solving the Two-Dimensional Diffusion in Fractal Heat Transfer, Thermal Science, 19(1), pp.99-103.
  • Yang,A.M., Yang,X.J. and Li,Z.B., (2013), Local Fractional series expansion method for Solving wave and diffusion Equations on Cantor sets, Abstract and Applied Analysis, 2013, pp.1-6.
  • Jafari,H. and Jassim,H.K., (2015), Application of the Local fractional Adomian Decomposition and Series Expansion Methods for Solving Telegraph Equation on Cantor Sets Involving Local Fractional Derivative Operators, Journal of Zankoy Sulaimani-Part A, 17(2), pp.15-22.
  • Jafari,H. and Jassim,H.K., (2014), Local Fractional Adomian Decomposition Method for Solving Two Dimensional Heat conduction Equations within Local Fractional Operators, Journal of Advance in Mathematics, 9(4), pp.2574-2582.
  • Wang,S.Q., Yang,Y.J. and Jassim,H.K., (2014), Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative, Abstract and Applied Analysis, 2014, pp.1-7.
  • Yan,S.P., Jafari,H. and Jassim,H.K., (2014), Local Fractional Adomian Decomposition and Function Decomposition Methods for Solving Laplace Equation within Local Fractional Operators, Advances in Mathematical Physics, 2014, pp.1-7.
  • Jafari,H. and Jassim,H.K., (2014), Local Fractional Laplace Variational Iteration Method for Solving Nonlinear Partial Differential Equations on Cantor Sets within Local Fractional Operators, Journal of Zankoy Sulaimani-Part A, 16(4), pp.49-57.
  • Jassim, H. K., Unlu, C., Moshokoa, S. P. and Khalique, C. M., (2015), Local Fractional Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators, Mathematical Problems in Engineering, 2015, pp. 1-9.
  • Jafari,H. and Jassim,H.K., Moshokoa,S.P., Ariyan,V.M. and Tchier,F., (2016), Reduced differential transform method for partial differential equations within local fractional derivative operators, Ad- vances in Mechanical Engineering, 8(4), pp.1-6.
  • Jafari,H. and Jassim,H.K., (2015), Numerical Solutions of Telegraph and Laplace Equations on Cantor Sets Using Local Fractional Laplace Decomposition Method , International Journal of Advances in Applied Mathematics and Mechanics, 2(3), pp.144-151.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

H. K. Jassım Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 7 Sayı: 1

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