# Solution of Linear Fractional Systems with Variable Coefficients

## TL;DR

This paper develops a method using the generalized Peano--Baker series to explicitly solve linear fractional differential systems with variable coefficients, including initial value problems involving Riemann--Liouville and Caputo derivatives.

## Contribution

It introduces a novel approach to derive explicit solutions for variable coefficient linear fractional differential systems using the generalized Peano--Baker series.

## Key findings

- Explicit solutions obtained for homogeneous and inhomogeneous cases
- State-transition matrix constructed for variable coefficient systems
- Theoretical results validated with examples

## Abstract

The paper deals with the initial value problem for linear systems of FDEs with variable coefficients involving Riemann--Liouville and Caputo derivatives. The technique of the generalized Peano--Baker series is used to obtain the state-transition matrix. Explicit solutions are derived both in the homogeneous and inhomogeneous case. The theoretical results are supported by examples.