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Advancing the Application of the Rayleigh-Schrödinger Method for Identifying Key Parameters in Fractional-Order Begley–Torvik Type Models

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  • Andrey Sedelnikov

    (Department of Metal Forming, Institute of Aviation and Rocket and Space Technology, Samara National Research University, 34 Moskovskoye Shosse, Samara 443086, Russia)

  • Hedi Aleroeva

    (Department of Metal Forming, Institute of Aviation and Rocket and Space Technology, Samara National Research University, 34 Moskovskoye Shosse, Samara 443086, Russia)

Abstract

This study develops an extension of the classical Rayleigh–Schrödinger method for solving fractional-order differential equations. The primary objective is to derive the eigenvalues of a Begley–Torvik-type equation. The proposed analytical expression for the eigenvalues, obtained through this methodological advancement, shows excellent agreement with their exact values. This result is obtained by developing the Rayleigh–Schrödinger method and can be used for a wide range of applied problems. As an illustrative example, the Begley–Torvik type equation is used to describe the deformation-strength characteristics of polymer concrete and other modern granular road materials. It should be noted, however, that this represents just one of many potential applications for such fractional-order models.

Suggested Citation

  • Andrey Sedelnikov & Hedi Aleroeva, 2026. "Advancing the Application of the Rayleigh-Schrödinger Method for Identifying Key Parameters in Fractional-Order Begley–Torvik Type Models," Mathematics, MDPI, vol. 14(9), pages 1-9, April.
    • Handle: RePEc:gam:jmathe:v:14:y:2026:i:9:p:1437-:d:1927921
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