In this paper we are concerned with numerical methods to solve stochastic differential equations (SDEs), namely the Euler-Maruyama (EM) and Milstein methods. These methods are based on the truncated Ito-Taylor expansion. In our study we deal with a nonlinear SDE. We approximate to numerical solution using Monte Carlo simulation for each method. Also exact solution is obtained from Ito's formula. To show the effectiveness of the numerical methods, approximation solutions are compared with exact solution for different sample paths. And finally the results of numerical experiments are supported with graphs and error tables.

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This paper deals with the solution, stability character and asymptotic behavior of the rational difference equationwhere N0 = N ∪ {0}, α, β, γ ∈ R + , and the initial conditions x−1 and x0 are non zero real numbers such that their solutions are associated to generalized Padovan numbers. Also, we investigate the two-dimensional case of the this equation given byand this generalizes the results presented in [34].

By applying the concept (and theory) of fractionalq-calculus, we first define and introduce two newq-integral operators for certain analytic functions defined in the unit disc𝒰. Convexity properties of theseq-integral operators on some classes of analytic functions defined by a linear multiplier fractionalq-differintegral operator are studied. Special cases of the main results are also mentioned.

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