New aspects of fractional Biswas–Milovic model with Mittag-Leffler law

¹ Department of Mathematics, JECRC University, Jaipur 303905, Rajasthan, India.
² Department of Mathematics, University of Rajasthan, Jaipur 302004, Rajasthan, India.
³ Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukarιyurtcu Mahallesi Mimar Sinan Caddesi No: 4, 06790, Etimesgut, Turkey.
⁴ Institute of Space Sciences, Magurele, Bucharest, Romania.

^* Corresponding author: jagdevsinghrathore@gmail.com

Received: 27 September 2018
Accepted: 17 October 2018

Abstract

This article deals with a fractional extension of Biswas–Milovic (BM) model having Kerr and parabolic law nonlinearities. The BM model plays a key role in describing the long-distance optical communications. The fractional homotopy analysis transform technique (FHATM) is applied to examine the BM equation involving Atangana–Baleanu (AB) derivative of fractional order. The FHATM is constructed by using homotopy analysis technique, Laplace transform algorithm and homotopy polynomials. The numerical simulation work is performed with the aid of maple software package. In order to demonstrate the effects of order of AB operator, variables and parameters on the displacement, the results are shown graphically. The outcomes of the present investigation are very encouraging and show that the AB fractional operator is very useful in mathematical modelling of natural phenomena.