Abstract
A new definition of fractional derivative (NFD) with order α≥0, is developed in this paper. The new derivative has a smooth kernel that takes on two different representations for the temporal and spatial variables. The advantage of the proposed approach over traditional local theories and fractional models with a singular kernel lies in the possibility that there is a class of problems capable of describing scale-dependent fluctuations and material heterogeneities. Moreover, it has been shown that the NFD converges to the classical derivative faster than some other fractional derivatives.
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Cited by
3 articles.
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