A new smoothness result for Caputo-type fractional ordinary differential equations

TL;DR

This paper introduces a novel smoothness theorem for Caputo-type fractional differential equations, showing that solutions can be smoothed by subtracting an appropriate non-smooth function derived from available information.

Contribution

It provides a new theoretical result demonstrating that fractional differential equation solutions can be smoothed under certain conditions, enhancing understanding of their regularity.

Findings

Solutions belong to C^m after subtracting a suitable non-smooth function

The result applies to Caputo-type fractional differential equations

It advances the theoretical understanding of solution regularity

Abstract

We present a new smoothness result for Caputo-type fractional ordinary differential equations, which reveals that, subtracting a non-smooth function that can be obtained by the information available, a non-smooth solution belongs to $ C^m $ for some positive integer $ m $.