On the Boundary Functional of a Semi-Markov Process

Year 2024, Volume: 5 Issue: 2, 123 - 133, 31.07.2024

Elshan Ibayev

https://doi.org/10.54974/fcmathsci.1387316

Abstract

In this paper, we consider the semi-Markov random walk process with negative drift, positive
jumps. An integral equation for the Laplace transform of the conditional distribution of the boundary
functional is obtained. In this work, we define the residence time of the system by generalized exponential
distributions with different parameters via fractional order integral equation. The purpose of this paper
is to reduce an integral equation for the Laplace transform of the conditional distribution of a boundary
functional of the semi-Markov random walk processes to fractional order differential equation with constant
coefficients.

Keywords

Laplace transform, random variable, semi-Markov random walk process, Riemann-Liouville fractional derivative

Ethical Statement

The author declares that the materials and methods used in her study do not require ethical committee

Supporting Institution

Institute of Control Systems

Thanks

We wish to express our thanks to Associate professor R. A Bandaliev for the formulation of the common problems in connection with fractional order differential equation

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