  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.
