# Existence of smooth solutions of multi-term Caputo-type fractional differential equations

## TL;DR

This paper investigates the existence of smooth solutions for multi-term Caputo fractional differential equations by transforming the problem into an integral equation and applying fixed point theory.

## Contribution

It provides new existence results for smooth solutions of multi-term Caputo fractional differential equations using Schauder fixed point theorem.

## Key findings

- Established existence of smooth solutions under certain conditions
- Transformed differential equations into Volterra-type integral equations
- Applied Schauder fixed point theorem for proofs

## Abstract

This paper deals with the initial value problem for the multi-term fractional differential equation. The fractional derivative is defined in the Caputo sense. Firstly the initial value problem is transformed into a equivalent Volterra-type integral equation under appropriate assumptions. Then new existence results for smooth solutions are established by using the Schauder fixed point theorem.