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Discrete fractional order systems have attracted more and more attention in recent years. Nabla Laplace transform is an important tool to deal with the problem of nabla discrete fractional order systems, but there is still much room for its development. In this paper, 14 lemmas are listed to conclude the existing properties and 14 theorems are developed to describe the innovative features. On one hand, these properties make the N-transform more effective and efficient. On the other hand, they enrich the discrete fractional order system theory
The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform. For the fi
We calculate exactly the Laplace transform of the Fr{e}chet distribution in the form $gamma x^{-(1+gamma)} exp(-x^{-gamma})$, $gamma > 0$, $0 leq x < infty$, for arbitrary rational values of the shape parameter $gamma$, i.e. for $gamma = l/k$ with $l
Taylor series is a useful mathematical tool when describing and constructing a function. With the series representation, some properties of fractional calculus can be revealed clearly. This paper investigates two typical applications: Lebiniz rule an
In this paper we prove that the Hankel multipliers of Laplace transform type on $(0,1)^n$ are of weak type (1,1). Also we analyze Lp-boundedness properties for the imaginary powers of Bessel operator on $(0,1)^n$.
The occurrence of digits 1 through 9 as the leftmost nonzero digit of numbers from real-world sources is distributed unevenly according to an empirical law, known as Benfords law or the first digit law. It remains obscure why a variety of data sets g