Scholarlink

Abstract <p>In this study, a semi-Markov random walk processes with negative drift, positive jumps and two delaying screen is investigated. The random variable—the numbers of the steps for the first moment of reaching level zero is introduced. We provide a mathematical modeling of the semi-Markov random walk processes with two delaying screens, expressed in general form through an integral equation. In this paper, the residence time of the system is given by the gamma distribution with parameters <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha&gt;0\)</EquationSource> <!--LobJMat2561144Bandaliyev-m1--> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\beta&gt;0\)</EquationSource> <!--LobJMat2561144Bandaliyev-m2--> </InlineEquation> resulting in the fractional order integral equation. The purpose of this paper is to reduce an integral equation for the generating function of the conditional distribution of the random variable to a fractional order differential equation.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

A Semi-Markov Random Walk Process and Its Connection with Fractional Order Differential Equation

  • 期刊论文

  • 发表日期：

    2025年12月1日

查看全文
  • R. A. Bandaliyev,
  • K. K. Omarova,
  • E. A. Ibayev

摘要

Abstract

In this study, a semi-Markov random walk processes with negative drift, positive jumps and two delaying screen is investigated. The random variable—the numbers of the steps for the first moment of reaching level zero is introduced. We provide a mathematical modeling of the semi-Markov random walk processes with two delaying screens, expressed in general form through an integral equation. In this paper, the residence time of the system is given by the gamma distribution with parameters \(\alpha>0\) and \(\beta>0\) resulting in the fractional order integral equation. The purpose of this paper is to reduce an integral equation for the generating function of the conditional distribution of the random variable to a fractional order differential equation.