Distributional framework for solving fractional differential equations

TL;DR

This paper investigates the solvability of a specific class of distributed order fractional differential equations using the framework of tempered distributions supported on the positive half-line.

Contribution

It introduces a distributional framework to analyze the solvability of fractional differential equations of a special form.

Findings

Established conditions for solvability within tempered distributions.

Provided a mathematical framework for distributed order fractional equations.

Extended the understanding of fractional differential equations in distribution spaces.

Abstract

We analyze solvability of a special form of distributed order fractional differential equations within the space of tempered distributions supported by the positive half-line.