Trapezoidal methods for fractional differential equations: theoretical and computational aspects

TL;DR

This paper explores various generalized trapezoidal methods for fractional differential equations, analyzing their theoretical properties and computational implementation, supported by numerical experiments to demonstrate their effectiveness and limitations.

Contribution

It introduces and compares different approaches to extend the trapezoidal method to fractional differential equations, focusing on theoretical analysis and computational efficiency.

Findings

Numerical experiments illustrate the potential of the methods.

Analysis reveals limitations in certain approaches.

Computational strategies improve efficiency of fractional differential equation solutions.

Abstract

The paper describes different approaches to generalize the trapezoidal method to fractional differential equations. We analyze the main theoretical properties and we discuss computational aspects to implement efficient algorithms. Numerical experiments are provided to illustrate potential and limitations of the different methods under investigation.