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The aim of this article is to establish a stochastic search algorithm for neural networks based on the fractional stochastic processes {๐ต๐ป๐ก,๐กโฅ0} with the Hurst parameter ๐ปโ(0,1). We define and discuss the properties of fractional stochastic processes, {๐ต๐ป๐ก,๐กโฅ0}, which generalize a standard Brownian motion. Fractional stochastic processes capture useful yet different properties in order to simulate real-world phenomena. This approach provides new insights to stochastic gradient descent (SGD) algorithms in machine learning. We exhibit convergence properties for fractional stochastic processes.