State dependent versions of the space-time fractional poisson process-Reference-Cited by-同舟云学术

State dependent versions of the space-time fractional poisson process

Published:2020-10-01 Issue:5 Volume:23 Page:1483-1505
ISSN:1314-2224
Container-title:Fractional Calculus and Applied Analysis
language:en
Short-container-title:

Author:

Kataria Kuldeep Kumar¹,Vellaisamy Palaniappan²

Affiliation:

1. Dept. of Mathematics , Indian Institute of Technology Bhilai , Raipur , 492015 , India

2. Department of Mathematics , Indian Institute of Technology Bombay , Mumbai , 400076 , India

Abstract

Abstract In this paper, we introduce and study two counting processes by considering state dependency on the order of fractional derivative as well as on the exponent of backward shift operator involved in the governing difference-differential equations of the state probabilities of space-time fractional Poisson process. The Adomian decomposition method is employed to obtain their state probabilities and then their Laplace transforms are evaluated. Also, the compound versions of these state dependent models are studied and the corresponding governing fractional integral equations of their state probabilities are obtained.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/fca-2020-0074/pdf

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