Tangent nonlinear equation in context of fractal fractional operators with nonsingular kernel

Zain Ul Abadin Zafar; Ndolane Sene; Hadi Rezazadeh; Nafiseh Esfandian

doi:10.1007/s40096-021-00403-7

Tangent nonlinear equation in context of fractal fractional operators with nonsingular kernel

Math Sci (Karaj). 2022;16(2):121-131. doi: 10.1007/s40096-021-00403-7. Epub 2021 Apr 27.

Authors

Zain Ul Abadin Zafar¹, Ndolane Sene², Hadi Rezazadeh³, Nafiseh Esfandian⁴

Affiliations

¹ Department of Mathematics, Faculty of Sciences, University of Central Punjab, Lahore, Pakistan.
² Laboratoire Lmdan, Dé partement de Mathé matiques de la Dé cision, Faculté des Sciences Economiques et Gestion, Université Cheikh Anta Diop de Dakar, BP 5683 Dakar Fann, Senegal.
³ Faculty of Modern Technologies Engineering, Amol University of Special Modern Technologies, Amol, Iran.
⁴ Department of Electrical Engineering, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran.

Abstract

In this manuscript, we investigate the approximate solutions to the tangent nonlinear packaging equation in the context of fractional calculus. It is an important equation because shock and vibrations are unavoidable circumstances for the packaged goods during transport from production plants to the consumer. We consider the fractal fractional Caputo operator and Atangana-Baleanu fractal fractional operator with nonsingular kernel to obtain the numerical consequences. Both fractal fractional techniques are equally good, but the Atangana-Baleanu Caputo method has an edge over Caputo method. For illustrations and clarity of our main results, we provided the numerical simulations of the approximate solutions and their physical interpretations. This paper contributes to the new applications of fractional calculus in packaging systems.

Keywords: Atangana–Baleanu fractal fractional operator; Fractal fractional caputo operator; Tangent nonlinear packaging equation.