COMPARISON OF SOLITON BEHAVIOR OF LAKSHMANAN-PORSEZIAN-DANIEL MODEL FOR TWO KINDS OF FRACTIONAL DERIVATIVES

The analytical soliton solutions of the time-space fractional Lakshmanan-Porsezian-Daniel (TSFLPD) model are obtained in this research paper. The proposed model is investigated using two new definitions of fractional derivatives including β-derivative and M-truncated derivative (MTD). The modified auxiliary equation method is used to obtain the analytical solutions of the proposed model. There are distinct patterns of soliton solutions observed among acquired solutions. The constructed solutions include kink solitons, dark solitons and some other singular soliton solutions. The constructed analytical solutions are graphically shown using analytical software. Two and three-dimensional graphs of obtained solutions are plotted. The effects of fractional derivatives 2D-line graphs are utilized for the comparison of results of proposed derivatives.