Open AccessSOME PROPERTIES OF FRACTIONAL BURGERS EQUATION
Author(s) -
Paulius Miškinis
Publication year - 2002
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2002.9637187
Subject(s) - burgers' equation , mathematics , generalization , fractional calculus , order (exchange) , integer (computer science) , transformation (genetics) , conservation law , mathematical analysis , pure mathematics , mathematical physics , derivative (finance) , partial differential equation , biochemistry , chemistry , finance , computer science , economics , gene , programming language , financial economics
The fractional generalization of a one‐dimensional Burgers equationwith initial conditionsɸ(x, 0) = ɸ0(x); ɸt(x,0) = ψ0 (x), where ɸ = ɸ(x,t) ∈ C2(Ω): ɸt = δɸ/δt; aDx p is the Riemann‐Liouville fractional derivative of the order p; Ω = (x,t) : x ∈ E 1, t > 0; and the explicit form of a particular analytical solution are suggested. Existing of traveling wave solution and conservation laws are considered. The relation with Burgers equation of integer order and properties of fractional generalization of the Hopf‐Cole transformation are discussed.