New modied Atangana-Baleanu fractional derivative applied to solve nonlinear fractional dierential equations

The main goal of this work is to present a new modified version of the Atangana-Baleanu fractional derivative with Mittag-Leffler non-singular kernel and strong memory. This proposal presents important advantages when specific initial conditions are impossed. The new modified version of the Atangana-Baleanu fractional derivative with Mittag-Leffler non-singular kernel has been constructed considering the fulfillment of the initial conditions with special interest because they are decisive in the obtaintion of analytical and numerical solutions of the fractional differential equations. The advantage of this new fractional derivative in the fulfilling of initial conditions plays a central role for the implementation of different perturbative analytical methods, such as the homotopy perturbation method and the modified homotopy perturbation method. These methods will be applied to solve nonlinear fractional differential equations. This novel modified derivative can be applied in the future in different mathematical modeling areas where satisfy the initial conditions is of great relevance to get more accurate description of real-world problems.

Automated summary

The main goal of this work is to propose a new modified version of the Atangana-Baleanu fractional derivative with Mittag-Leffler non-singular kernel and strong memory. This modification is advantageous for specific initial conditions and can be applied in solving nonlinear fractional differential equations using perturbative analytical methods. The fulfillment of initial conditions plays a central role in obtaining accurate solutions and the new fractional derivative can contribute to more accurate mathematical modeling in various fields.