Research Papers

Time–Space Fractional Burger's Equation on Time Scales

[+] Author and Article Information
A. Neamaty

Department of Mathematics,
University of Mazandaran,
P.O. Box 47416-95447,
Pasdaran Street,
Babolsar 47416-95447, Iran
e-mail: namaty@umz.ac.ir

M. Nategh

Department of Mathematics,
University of Mazandaran,
P.O. Box 47416-95447,
Pasdaran Street,
Babolsar 47416-95447, Iran
e-mail: m.nategh@stu.umz.ac.ir

B. Agheli

Department of Mathematics,
Qaemshahr Branch,
Islamic Azad University,
P.O. Box 163,
Qaemshahr 163, Iran
e-mail: b.agheli@qaemshahriau.ac.ir

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received June 15, 2015; final manuscript received November 10, 2015; published online February 9, 2017. Assoc. Editor: Gabor Stepan.

J. Comput. Nonlinear Dynam 12(3), 031022 (Feb 09, 2017) (6 pages) Paper No: CND-15-1165; doi: 10.1115/1.4032258 History: Received June 15, 2015; Revised November 10, 2015

This paper deals with a newly born fractional derivative and integral on time scales. A chain rule is derived, and the given indefinite integral is being discussed. Also, an application to the traffic flow problem with a fractional Burger's equation is presented.

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Chen, W. , 2006, “ Time-Space Fabric Underlying Anomalous Diffusion,” Chaos, Solitons Fractals, 28(4), pp. 923–929. [CrossRef]
Hilger, S. , 1990, “ Analysis on Measure Chain—A Unified Approach to Discrete and Continuous Calculus,” Results Math., 18(1–2), pp. 18–56. [CrossRef]
Hilger, S. , 1997, “ Differential and Difference Calculus-Unified,” Theory Methods Appl., 30(5), pp. 2683–2694. [CrossRef]
Benkhettou, N. , Brito da Cruz, A. M. C. , and Torres, D. F. M. , 2015, “ A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration,” Signal Process., 107, pp. 230–237. [CrossRef]
Buslaev, A. P. , Gasnikov, A. V. , and Yashina, M. V. , 2012, “ Selected Mathematical Problems of Traffic Flow Theory,” Int. J. Comput. Math., 89(3), pp. 409–432. [CrossRef]
Gelfand, I . M. , 1959, “ Some Problems in the Theory of Quasilinear Equations,” UMN, 14(2), pp. 87–158 (translation).
Haight, F. A. , 1963, Mathematical Theories of Traffic Flow, Academic Press, New York.
Nagatani, T. , Emmerich, H. , and Nakanish, K. , 1998, “ Burger's Equation for Kinetic Clustering in Tracow,” Physica A, 255(1–2), pp. 158–162. [CrossRef]
Rothery, R. W. , 1992, “ Car Following Models,” Traffic flow Theory (Transportation Research Board), Vol. 165, N. Gartner , C. J. Messer , and A. K. Rathi , eds., U.S. Department of Transportation, Washington, DC, pp. 1–41.
Bohner, M. , and Peterson, A. , 2001, Dynamic Equations on Time Scales, Birkhäuser, Boston, MA.
Hallenbeck, M. , Rice, M. , Smith, B. , Cornell-Martinez, C. , and Wilkinson, J. , 1997, “ Vehicle Volume Distributions by Classification,” Report No. FHWA-PL-97-025.


Grahic Jump Location
Fig. 1

Density behind the fourth traffic light: u(x4, t) (Reprinted with permission from Hallenbeck et al., “Vehicle Volume Distributions by Classification” [11] Washington State Transportation Center)



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