Regularity of solutions for singular fractional differential equation

TL;DR

This paper investigates the regularity properties of positive solutions to nonlinear fractional differential equations with singular weights, introducing a new Banach space to analyze solutions that may not be integrable.

Contribution

It introduces a novel Banach space framework for studying regularity of solutions with singular weights in fractional differential equations.

Findings

Established regularity results for solutions with singular weights.

Provided an example of a singular weight not in L^1.

Demonstrated the applicability of the new Banach space approach.

Abstract

In this work, we study the regularity of positive solutions for nonlinear fractional differential equation with a singular weight. We define the new Banach space and use this space to show the regularity. We also give an example with a singular weight which may not be in $L^1.$