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Mathematical modeling of the semi‐Markovian random walk processes with jumps and delaying screen by means of a fractional order differential equation
Author(s) -
Bandaliyev Rovshan A.,
Nasirova Tamilla I.,
Omarova Konul K.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5328
Subject(s) - mathematics , laplace transform , markov process , integro differential equation , random walk , differential equation , stochastic differential equation , laplace–stieltjes transform , integral equation , mathematical analysis , laplace's equation , markov chain , order (exchange) , first order partial differential equation , statistics , fourier transform , fourier analysis , finance , fractional fourier transform , economics
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.