Mathematical modeling of the semi-Markovian random walk processes with jumps and delaying screen by means of a fractional order differential equation

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
Bandaliyev R.A. 1, 3 , Nasirova T.I.2 , Omarova K.K.2
Publisher
John Wiley and Sons Ltd
Number of issue
18
Language
English
Pages
9301-9311
Status
Published
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
Short link
https://repository.rudn.ru/en/records/article/record/36205/
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