Modeling with Fractional Laplace Transform by Difference Operator

2020 ◽  
Vol 6 (4) ◽  
pp. 263-271
Keyword(s):  
Laplace Transform ◽  
Difference Operator

scholarly journals n-Dimensional Fractional Frequency Laplace Transform by the Inverse Difference Operator

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
M. Meganathan ◽  
Thabet Abdeljawad ◽  
G. Britto Antony Xavier ◽  
Fahd Jarad
Keyword(s):  
Laplace Transform ◽  
Difference Operator ◽  
Extensive Literature ◽  
Fractional Frequency ◽  
Research Article ◽  
The Laplace Transform

With the study of extensive literature on the Laplace transform with one and two variables and its properties, applications are available, but there is no work on n-dimensional Laplace transform. In this research article, we define n-dimensional fractional frequency Laplace transform with shift values. Several theorems are derived with properties of the Laplace transform. The results are numerically analyzed and discussed through MATLAB.

scholarly journals Fractional frequency Laplace transform by inverse difference operator with shift value

2019 ◽  
Vol 3(2019) (1) ◽  
pp. 121-128 ◽  
Author(s):  
Sandra Pinelas ◽  
◽  
Meganathan Murugesan ◽  
Britto Antony Xavier Gnanaprakasam Gnanaprakasam ◽  
◽  
...  
Keyword(s):  
Laplace Transform ◽  
Difference Operator ◽  
Fractional Frequency

scholarly journals A general quantum Laplace transform

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Enas M. Shehata ◽  
Nashat Faried ◽  
Rasha M. El Zafarani
Keyword(s):  
Continuous Function ◽  
Laplace Transform ◽  
Difference Equations ◽  
Difference Operator ◽  
General Quantum ◽  
Quantum Difference

Abstract In this paper, we introduce a general quantum Laplace transform $\mathcal{L}_{\beta }$ L β and some of its properties associated with the general quantum difference operator ${D}_{\beta }f(t)= ({f(\beta (t))-f(t)} )/ ({ \beta (t)-t} )$ D β f ( t ) = ( f ( β ( t ) ) − f ( t ) ) / ( β ( t ) − t ) , β is a strictly increasing continuous function. In addition, we compute the β-Laplace transform of some fundamental functions. As application we solve some β-difference equations using the β-Laplace transform. Finally, we present the inverse β-Laplace transform $\mathcal{L}_{\beta }^{-1}$ L β − 1 .

The extinction time of a general birth and death process with catastrophes

1986 ◽  
Vol 23 (04) ◽  
pp. 851-858 ◽  
Author(s):  
P. J. Brockwell
Keyword(s):  
Laplace Transform ◽  
Size Distribution ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Death Process ◽  
Extinction Time ◽  
Birth And Death Process ◽  
Different Types ◽  
The Laplace Transform ◽  
Necessary And Sufficient

The Laplace transform of the extinction time is determined for a general birth and death process with arbitrary catastrophe rate and catastrophe size distribution. It is assumed only that the birth rates satisfyλ0= 0,λj> 0 for eachj> 0, and. Necessary and sufficient conditions for certain extinction of the population are derived. The results are applied to the linear birth and death process (λj=jλ, µj=jμ) with catastrophes of several different types.

The Resolvent Operator

2017 ◽  
Author(s):  
Charles L. Epstein ◽  
Rafe Mazzeo
Keyword(s):  
Cauchy Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Heat Kernel ◽  
Resolvent Operator ◽  
Contour Integration ◽  
Resolvent Kernel ◽  
The Laplace Transform ◽  
Elliptic Estimates ◽  
The Resolvent Operator

This chapter describes the construction of a resolvent operator using the Laplace transform of a parametrix for the heat kernel and a perturbative argument. In the equation (μ‎-L) R(μ‎) f = f, R(μ‎) is a right inverse for (μ‎-L). In Hölder spaces, these are the natural elliptic estimates for generalized Kimura diffusions. The chapter first constructs the resolvent kernel using an induction over the maximal codimension of bP, and proves various estimates on it, along with corresponding estimates for the solution operator for the homogeneous Cauchy problem. It then considers holomorphic semi-groups and uses contour integration to construct the solution to the heat equation, concluding with a discussion of Kimura diffusions where all coefficients have the same leading homogeneity.

Measuring the error of dynamic hedging: a Laplace transform approach

2009 ◽  
Vol 13 (2) ◽  
pp. 47-72 ◽  
Author(s):  
Flavio Angelini ◽  
Stefano Herzel
Keyword(s):  
Laplace Transform ◽  
Dynamic Hedging
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