In this paper, we investigate the semi-Markovian random walk processes with jumps and delaying screen in zero. The Laplace transform on time, Laplace- Stieltjes transform on phase of the conditional distribution of semi-Markovian random walk processes with jumps is found. We get a mathematical modeling of the semi-Markov random walk processes with a delaying screen in zero, given in general form by means of integral equation. In this paper, the residence time of the system is given by the gamma distribution with the parameters α and β resulting in a fractional order integral equation. The purpose of this paper is to reduce the fractional order integral equation to a fractional order differential equation. Finally, we find the exact solution of fractional order differential equation. © 2018 John Wiley & Sons, Ltd.

Authors

Publisher

John Wiley and Sons Ltd

Number of issue

18

Language

English

Pages

9301-9311

Status

Published

DOI

Volume

41

Year

2018

Organizations

^{1}Mathematical Analysis Department, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan^{2}Probabilistic Control Methods Laboratory, Institute of Control Systems of NAS of Azerbaijan, Baku, Azerbaijan^{3}S. M. Nikol'skii Institute of Mathematics, RUDN University, Moscow, Russian Federation

Keywords

fractional order differential equation; gamma distribution; Laplace transform; semi-Markovian random walk process

Date of creation

04.02.2019

Date of change

04.02.2019

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