On Nonlinear Hybrid Fractional Differential Equations with Atangana-Baleanu-Caputo Derivative

TL;DR

This paper develops a theoretical framework for nonlinear hybrid fractional differential equations involving the Atangana-Baleanu-Caputo derivative, including existence, uniqueness, and comparison results.

Contribution

It introduces the theory of inequalities for ABC-hybrid fractional differential equations and establishes foundational existence and comparison theorems.

Findings

Established the existence of solutions using fractional integral equations

Proved uniqueness and maximal/minimal solutions for the equations

Developed comparison results for ABC-hybrid fractional differential equations

Abstract

In this paper, we develop the theory of nonlinear hybrid fractional differential equations involving Atangana--Baleanu--Caputo (ABC) fractional derivative. We construct the equivalent fractional integral equation and establish the existence results through it. Further, we build up the theory of inequalities for ABC--hybrid fractional differential equations and use it to examine the uniqueness, existence of a maximal and minimal solution and the comparison results.