https://hal.archives-ouvertes.fr/hal-01766566/document

Special values of the bell polynomials of the second kind for some sequences and functions

http://ilitia.cua.uam.mx:8080/jspui/bitstream/123456789/866/1/Cubic-quartic%20bright%20optical%20solitons%20with%20improved%20Adomian%20decomposition%20method.pdf

Cubic-quartic bright optical solitons with improved Adomian decomposition method

Starting from the definition of fractional M/M/1 queue given in the reference by Cahoy et al in 2015 and M/M/1 queue with catastrophes given in the reference by Di Crescenzo et al in 2003, we define and study a fractional M/M/1 queue with catastrophes In particular, we focus our attention on the transient behaviour, in which the time-change plays a key role We first specify the conditions for the global uniqueness of solutions of the corresponding linear fractional differential problem Then, we provide an alternative expression for the transient distribution of the fractional M/M/1 model, the state probabilities for the fractional queue with catastrophes, the distributions of the busy period for fractional queues without and with catastrophes and, finally, the distribution of the time of the first occurrence of a catastrophe

https://www.mdpi.com/2227-7390/6/9/159/pdf

Fractional Queues with Catastrophes and Their Transient Behaviour

Saigo space–time fractional Poisson process via Adomian decomposition method

The Poisson process suitably models the time of successive events and thus has numerous applications in statistics, in economics, it is also fundamental in queueing theory. Economic applications include trading and nowadays particularly high frequency trading. Of outstanding importance are applications in insurance, where arrival times of successive claims are of vital importance. It turns out, however, that real data do not always support the genuine Poisson process. This has lead to variants and augmentations such as time dependent and varying intensities, for example. This paper investigates the fractional Poisson process. We introduce the process and elaborate its main characteristics. The exemplary application considered here is the Carmer–Lundberg theory and the Sparre Andersen model. The fractional regime leads to initial economic stress. On the other hand we demonstrate that the average capital required to recover a company after ruin does not change when switching to the fractional Poisson regime. We finally address particular risk measures, which allow simple evaluations in an environment governed by the fractional Poisson process.

/pdf/fractional-risk-process-in-insurance-2jdtvg18uy.pdf

Fractional risk process in insurance

In this paper, we discuss two simple parametrization methods for calculating
 Adomian polynomials for several nonlinear operators, which utilize the
 orthogonality of functions einx, where n is an integer. Some important
 properties of Adomian polynomials are also discussed and illustrated with
 examples. These methods require minimum computation, are easy to implement,
 and are extended to multivariable case also. Examples of different forms of
 nonlinearity, which includes the one involved in the Navier Stokes equation,
 is considered. Explicit expression for the n-th order Adomian polynomials are
 obtained in most of the examples.

/pdf/simple-parametrization-methods-for-generating-adomian-3k8rgjtfgz.pdf

Simple Parametrization Methods for Generating Adomian Polynomials

In this paper, we discuss two simple parametrization methods for calculating Adomian polynomials for several nonlinear operators, which utilize the orthogonality of functions einx, where n is an integer. Some important properties of Adomian polynomials are also discussed and illustrated with examples. These methods require minimum computation, are easy to implement, and are extended to multivariable case also. Examples of different forms of nonlinearity, which includes the one involved in the Navier Stokes equation, is considered. Explicit expression for the n-th order Adomian polynomials are obtained in most of the examples.

/pdf/simple-parametrization-methods-for-generating-adomian-e4jsmmd0yd.pdf

On densities of the product, quotient and power of independent subordinators

We obtain the distribution of the sum of independent Mittag–Leffler (ML) random variables which are not necessarily identically distributed. Firstly we discuss the corresponding known result for in...

K. K. Kataria

Papers

Saigo space–time fractional Poisson process via Adomian decomposition method

Simple Parametrization Methods for Generating Adomian Polynomials

Simple Parametrization Methods for Generating Adomian Polynomials

On densities of the product, quotient and power of independent subordinators

On the convolution of Mittag–Leffler distributions and its applications to fractional point processes