Analysis of Nonlinear Fractional Differential Equations Involving Atangana-Baleanu-Caputo Derivative

TL;DR

This paper investigates the properties of Atangana-Baleanu-Caputo fractional derivatives, deriving estimations and comparison results to establish existence of solutions for nonlinear fractional differential equations involving this derivative.

Contribution

It provides new estimations and comparison theorems for Atangana-Baleanu-Caputo derivatives, facilitating the analysis of solution existence in nonlinear fractional differential equations.

Findings

Derived estimations of the Atangana-Baleanu-Caputo derivative at extreme points

Established comparison results for nonlinear fractional differential equations

Proved existence of local, extremal, and global solutions

Abstract

In the present paper, we determine the estimations on Atangana-Baleanu-Caputo fractional derivative at extreme points. With the assistance of the estimations obtained, we derive the comparison results. Peano's type existence results established for nonlinear fractional differential equations involving Atangana-Baleanu-Caputo fractional derivative. The acquired comparison results are then utilized to deal with the existence of local, extremal and global solution.