CMMSE: Application of the Parametrization Method to Solving Boundary Value Problems for Fractional Equations


Usmanov K. Nazarova K.
2026John Wiley and Sons Ltd

Mathematical Methods in the Applied Sciences
2026

This paper studies a boundary value problem for systems of fractional-order differential equations. The work aims to solve a fractional-order differential equation using the parameterization method developed by Professor D. Dzhumabayev. Based on this method, an algorithm for finding a solution to the problem under study is proposed, and the solvability of the problem under study is determined. For this, the (Formula presented.) condition is taken, and the segment under consideration is divided into (Formula presented.) parts. The values of the function tapering at the initial points of each segment are designated by the parameter (Formula presented.) so that a replacement (Formula presented.) is made on each interval. The replacement of variables formally divides the problem into two components: A Cauchy problem for a fractional-order differential equation and a system of linear equations with regard to the parameters entered. Therewith, a closed system for a pair (Formula presented.) is obtained. By this means, an algorithm for finding a solution is obtained, and the convergence of this algorithm is proven.

algorithm , boundary value problem , Cauchy problem , fractional derivative , linear equations system , parameter , parameterization method

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Khoja Akhmet Yassawi International Kazakh–Turkish University, Turkistan, Kazakhstan

Khoja Akhmet Yassawi International Kazakh–Turkish University

10 лет помогаем публиковать статьи Международный издатель

Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026