  In this paper, a modified nonlinear Schr\"{o}dinger equation with
spatio-temporal 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 Schr\"{o}dinger equation with
spatio-temporal dispersion. The approximate analytical solutions using the
proposed generalized method in the sense of Caputo fractional derivative and
conformable derivatives are obtained and compared with each other graphically.

General Mathematics