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

ABSTRACT 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 condition is taken, and the segment under consideration is divided into parts. The values of the function tapering at the initial points of each segment are designated by the parameter so that a replacement 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 is obtained. By this means, an algorithm for finding a solution is obtained, and the convergence of this algorithm is proven.