Numerical Methods for Fractal-Fractional Differential Equations and Engineering

9Application of Fractal-Fractional Operators to a Chaotic Model

DOI: 10.1201/9781003359258-9

9.1 INTRODUCTION

The concept of local differentiation and integration is known to be the classical differentiation. The classical differentiation is further extended into the concept of fractional derivative with Caputo type with local and singular kernel. Further, the idea was extended in the sense of Caputo-Fabrizio operator with non-local and singular kernel. Moreover, the fractional calculus was extended to have operator with non-local and non-singular kernel known as Atangana-Baleanu operator. The beginning of the fractional calculus was the use of the power law kernel for the classical derivative. This concept has been used by the researchers ...