Fractional activation functions in feedforward artificial neural networks

Fractional calculus is an important tool for analysis, including physics, biology and artificial intelligence. For some functions, alternative fractional definitions have been developed - the exponential function, trigonometric functions, hyperbolic tangent. But for others, like the logistic sigmoid function, fractional equivalents are not yet studied. Most of the mentioned functions are used as activation functions in artificial neural networks. Using the fractional activation functions provides the networks with more tunable hyperparameters. In this paper, analysis of some fractional functions is made, and the effects of different choices of function parameter values is examined in terms of learning and precision of feed-forward artificial neral networks.