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In this paper, we give the results of the theoretical study concerning the combined kinetic charging of the particles on the precipitating electrode in a corona field by taking into account contact charging. We derive some mathematical equations that allow us to determine the limit charge values on the particles and the charging kinetics of the particles. It has been demonstrated that the limit charge value on the particle can be less than the value calculated using the Pauthenier theory. In the case when the time constant ratio of contact and field charging mechanisms is equal to the ratio of the maximum charges of these charging mechanisms, we find that the sign of the limit charge on the particle has changed.

Fractional calculus presents a new perspective for solution of scientific and engineering problems. There are still many fields where fractional calculus promise fresh understanding of real world problems. In this study, we present an investigation on fractional order motion, where we extend our comprehension from velocity and acceleration concepts to a fuzzy velocity and acceleration domains. Here, fundamentally, we suggest a debate on interpretation of fractional-order derivative system on the bases of integer-order derivative knowledge. We observed that the continuous fractional-order motion equation set can be considered to cover the discrete integer-order motion equation set and physical meaning of fractional-order motion systems can be better understood by using a fuzzy conceptualization of integer-order derivative systems according to the dissimilarity metric.

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