Subfield method for equations with fractional and differential operator

When studying some physical processes, such as, for example, the study of force directed on an electric charge moving at a speed close to light in a background magnetic field, there is a necessity to use derivatives of fractional orders, and with the development of science and technology such studies become most relevant. Such problems lead to the necessity of building a model of the process with further numerical realization, which requires justification of application of the approximation apparatus and finding the approximation accuracy.The work presents the results of theoretical justification of application of the method of subfields for finding numerical solutions of equations with fractional differentiation operators.The structure of the numerical solution and an estimate of the error of the approximate solution by the metric of the energy space generated by the fractional differentiation operator are determined. As a test case for a particular case of fractional differential equation, the computational scheme of the method is built.The results of the article can serve as both theoretical and practical applications in solving boundary value problems that lead to differential equations with fractional order derivatives.