Solvability of a boundary value problem for fractional-order differential equations with involution

K. I. Usmanov, Kulzina Zh. Nazarova, Zhazira Yerkisheva

2025

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DOI 10.47533/2025.1606-146x.3-23

Data confidence 70 medium

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Abstract

This paper considers a boundary value problem for a fractional-order differential equation in the sense of Caputo with an involutive transformation. The parametrization method of Professor D. Dzhumabaev is applied to solve the problem. A parameter is introduced, and a substitution is performed. Thus, the considered problem is divided into two parts: the Cauchy problem for a fractional-order differential equation and a linear equation with respect to the introduced parameter. The parameters are chosen in such a way that the Cauchy problem for the fractional-order differential equation has a classical solution. By applying certain transformations, a unique solution to the Cauchy problem is determined. Based on the unique solvability of the obtained equation concerning the introduced parameter, the solvability of the studied problem is established.