Extraction of new optical solitons of conformable time fractional generalized RKL equation via quadrupled power-law of self-phase modulation

Abstract

In the current work, we investigate the optical solitons and exact solutions for the conformable time fractional generalized Radhakrishnan–Kundu–Lakshmanan (GRKL)equation with the polynomial law of nonlinearity which represent the mathematical model of pulse propagation in a nonlinear medium in optical fibers. The modified extended direct algebraic method is presented to get the exact solutions for this model. Many varieties of traveling wave solutions are established like, solitons (bright, dark, singular, combo singular-dark), combo periodic solutions, periodic solutions, Jacobi elliptic solutions, exponential solutions and Weierstrass elliptic solutions. The impact of the fractional derivative is illustrated graphically using examples of some of the retrieved solutions with various values of fractional order.