A new criterion for multivalent starlike functions

Wang, Zhigang; Xu, Nan

doi:10.2298/aadm0802183w

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“…Equation (1) with α = 1 is a special case of the KPP equation. The classical KPP equation has been investigated using many methods including the two ansätzes (Bernoulli equation and Riccati equation), [27] the discrimination algorithm, [28] the G ′ /Gexpansion method, [29] and so on. The time-and spacefractional KPP equations with a = 2, b = c = 0 were studied by the homotopy perturbation method.…”

Section: Introductionmentioning

confidence: 99%

Approximate Solutions of Nonlinear Fractional Kolmogorov—Petrovskii—Piskunov Equations Using an Enhanced Algorithm of the Generalized Two-Dimensional Differential Transform Method

Song¹,

Wang²

2012

Commun. Theor. Phys.

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By constructing the iterative formula with a so-called convergence-control parameter, the generalized two-dimensional differential transform method is improved. With the enhanced technique, the nonlinear fractional Kolmogorov-Petrovskii-Piskunov equations are dealt analytically and approximate solutions are derived. The results show that the employed approach is a promising tool for solving many nonlinear fractional partial differential equations. The algorithm described in this work is expected to be employed to solve more problems in fractional calculus.

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Section: Introductionmentioning

confidence: 99%