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<p>In this paper, we study a scalar linear fractional differential equation with random inhomogeneous parts. The analysis is performed by means of the mean square calculus using the Caputo derivative. A series solution of this equation is derived with the help of a mean square version of the geometric series and the Laplace transform. This series solution is shown to be mean square convergent for all positive real numbers. In addition, we provide approximations of the main statistical functions of the stochastic solution process, such as its mean and variance. Our theoretical findings are illustrated with two examples.</p>

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Constructing mean square series solutions for a class of one-dimensional linear fractional random differential equations via the Laplace transform

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • L. Villafuerte,
  • A. Treviño

摘要

In this paper, we study a scalar linear fractional differential equation with random inhomogeneous parts. The analysis is performed by means of the mean square calculus using the Caputo derivative. A series solution of this equation is derived with the help of a mean square version of the geometric series and the Laplace transform. This series solution is shown to be mean square convergent for all positive real numbers. In addition, we provide approximations of the main statistical functions of the stochastic solution process, such as its mean and variance. Our theoretical findings are illustrated with two examples.