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# Lie group classifications and exact solutions for time-fractional Burgers equation

11/2010;

Source: arXiv

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**ABSTRACT:**An existence and uniqueness theorem is proved for a quasilinear stochastic evolution equation with an additive noise in the form of a stochastic integral with respect to a Hilbert space-valued fractional Borwnian motion. Ideas of the finite-dimensional approximation by the Galerkin method are used.Statistics [?] Probability Letters 01/1999; 41(4):337-346. · 0.53 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**It is shown that, by using Taylor’s series of fractional order, the stochastic differential equation , where b(t,a) is a fractional Brownian motion of order a, can be converted into an equation involving fractional derivative, therefore a solution expressed in terms of the Mittag–Leffler function.Applied Mathematics Letters 01/2005; · 1.50 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The paper gives some results and improves the derivation of the fractional Taylor's series of nondifferentiable functions obtained recently in the form f (χ + h) = Eα (hαDχα)f(χ), 0 α ≤ 1, where Eα is the Mittag-Leffier function. Here, one defines fractional derivative as the limit of fractional difference, and by this way one can circumvent the problem which arises with the definition of the fractional derivative of constant using Riemann-Liouville definition. As a result, a modified Riemann-Liouville definition is proposed, which is fully consistent with the fractional difference definition and avoids any reference to the derivative of order greater than the considered one's. In order to support this F-Taylor series, one shows how its first term can be obtained directly in the form of a mean value formula. The fractional derivative of the Dirac delta function is obtained together with the fractional Taylor's series of multivariate functions. The relation with irreversibility of time and symmetry breaking is exhibited, and to some extent, this F-Taylor's series generalizes the fractional mean value formula obtained a few years ago by Kolwantar.Computers & Mathematics with Applications 05/2006; · 2.07 Impact Factor

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