# A Collocation Method in Spline Spaces for the Solution of Linear Fractional Dynamical Systems

## TL;DR

This paper introduces a collocation method using spline spaces to efficiently solve linear fractional dynamical systems, with proven convergence and demonstrated numerical results.

## Contribution

It presents a novel collocation approach in spline spaces specifically designed for fractional dynamical systems, including convergence proof and practical numerical validation.

## Key findings

- Efficient evaluation of collocation matrices using B-spline derivatives
- Convergence of the proposed collocation method established
- Numerical results demonstrate method effectiveness

## Abstract

We used a collocation method in refinable spline space to solve a linear dynamical system having fractional derivative in time. The method takes advantage of an explicit derivation rule for the B-spline basis that allows us to efficiently evaluate the collocation matrices appearing in the method. We proof the convergence of the method. Some numerical results are shown.