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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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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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