# A novel class of fractional adams method for solving uncertain fractional differential equation

## TL;DR

This paper introduces a new fractional Adams numerical method for solving uncertain fractional differential equations, improving accuracy and efficiency over existing methods, with stability analysis and practical simulations demonstrating its effectiveness.

## Contribution

A novel fractional Adams method derived from interval weighting extends predictor-corrector approaches for UFDE, with stability and error analysis and enhanced numerical performance.

## Key findings

- Higher accuracy in numerical simulations
- Extended predictor-corrector to higher order
- Validated stability and error bounds

## Abstract

Uncertain fractional differential equation (UFDE) is a kind of differential equation about uncertain process. As an significant mathematical tool to describe the evolution process of dynamic system, UFDE is better than the ordinary differential equation with integer derivatives because of its hereditability and memorability characteristics. However, in most instances, the precise analytical solutions of UFDE is difficult to obtain due to the complex form of the UFDE itself. Up to now, there is not plenty of researches about the numerical method of UFDE, as for the existing numerical algorithms, their accuracy is also not high. In this research, derive from the interval weighting method, a class of fractional adams method is innovatively proposed to solve UFDE. Meanwhile, such fractional adams method extends the traditional predictor-corrector method to higher order cases. The stability and truncation error limit of the improved algorithm are analyzed and deduced. As the application, several numerical simulations (including $\alpha$-path, extreme value and the first hitting time of the UFDE) are provided to manifest the higher accuracy and efficiency of the proposed numerical method.