New Chaotic Attractor Captured with Fractal-Fractional Differential and Integral Operators

Abstract

Differential operators based on convolution have been recognized as powerful mathematical operators able to depict and capture chaotic behaviors, especially those that are not able to be depicted using classical differential and integral operators. While these differential operators have being applied with great success in many fields of science, especially in the case of dynamical systems, we have to confess that they were not able depict some chaotic behaviors, especially those with additionally similar patterns. To solve this issue, a new class of differential and integral operators were proposed and applied in a few problems. In this paper, we aim to depict chaotic behavior using the newly defined differential and integral operators with fractional order and fractal dimension. Additionally, we introduce a new chaotic operators with strange attractors.