The method of numerical and analytical solution of linear differential equations with non-integer derivatives in Caputo order and with variable coefficients

TL;DR

This paper presents an approximation-operational method for solving linear differential equations with fractional and mixed orders, including variable coefficients, demonstrated through computational experiments in Mathematica.

Contribution

It introduces a versatile approximation-operational approach applicable to fractional and mixed order differential equations with variable coefficients.

Findings

Method effectively solves fractional differential equations with variable coefficients.

Computational experiments validate the approach in Mathematica.

Applicable to both fractional and mixed order differential equations.

Abstract

The application of the approximation-operational approach to solving linear differential equations of fractional order with variable coefficients is considered. It is shown that the method can also be applied to solving differential equations of both fractional and mixed orders. Computational experiments performed in a Mathematica (TM) software environment