New approximate analytical solutions for the nonlinear fractional Schrödinger equation with second‐order spatio‐temporal dispersion via double Laplace transform method - Kaabar, Mohammed K. A.; Martínez, Francisco; Gómez‐Aguilar, José Francisco; Ghanbari, Behzad; Kaplan, Melike; Günerhan, Hatira (Wiley, 2021)
In this paper, a modified nonlinear Schrödinger equation with spatiotemporal dispersion is formulated in the senses of Caputo fractional derivative and conformable derivative. A new generalized double Laplace transform coupled with Adomian decomposition method has been defined and applied to solve the newly formulated nonlinear Schrödinger equation with spatiotemporal dispersion. The approximate analytical solutions are obtained and compared with each other graphically.
Keywords: nonlinear fractional Schrödinger equation; Caputo fractional derivative; double Laplace transform; Fractional derivatives and integrals; NLS equations (nonlinear Schrödinger equations); conformable derivative