Generalized fractal–fractional order problems under non-singular Mittag-Leffler kernel

Abstract

This manuscript analyzed the general investigation of the fractal–fractional mathematical problem under Atangana–Baleanu in the sense of Caputo (ABC) fractional operator having non-singular Mittag-Leffler kernel. For simplicity, the proposed general system has been divided into five compartments. The said problem has been checked for the existence and uniqueness of solution, by using the Krasnosilkii’s and Banach contraction theorem respectively. The considered fractal–fractional system is further changed with a small perturbation term for testing the concept of Ulam Hyer’s (UH) Stability. The approximate solution is obtained by applying the fractal–fractional Adams–Bashforth methods. The general problem is also investigated specifically in the illustrative example for the qualitative analysis and numerical solution by using the obtained scheme. The said example is graphically represented in different fractional-order and fractal dimensions along with chaotic behavior.