Existence results in the theory of fractional hybrid di erential equations of fractional orders

TL;DR

This paper establishes existence results for hybrid fractional integro-differential equations using fixed point theorems and differential inequalities, providing tools for analyzing solutions' behavior.

Contribution

It introduces new existence theorems for hybrid fractional equations and develops fundamental inequalities and comparison principles for qualitative analysis.

Findings

Existence of solutions proved under certain conditions

Development of differential inequalities for fractional equations

Comparison principle established for solution analysis

Abstract

In this paper, we study existence results for initial value problems for hybrid fractional integro-differential equations. Our investigation is based on the Dhage hybrid fixed point theorem. Some fundamental fractional differential inequalities are also established which are utilized to prove the existence of extremal solutions. Necessary tools are considered and the comparison principle is proved which will be useful for further study of qualitative behavior of solutions.