Fractional effects on solitons in a 1D array of rectangular ferroelectric nanoparticles

Abstract

ABSTRACT In this paper, we present non-local effects on solitons in a one-dimensional (1D) array of ferroelectric nanoparticles. Using the discrete tangent hyperbolic method, several fractional function solutions are obtained such as fractional hyperbolic, trigonometric and rational function solutions. As results, we derive many solitons such as dark, bright and rogue waves. We show that the fractional parameter α has an effect on the width and on the amplitude of the above-obtained solitons. Their width and their amplitude are modified by the value of the fractional parameter α. Fractional derivative has a memory effect on ferroelectric nanoparticles. Applications of the obtained results are also presented.