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New approximate analytical solutions for the nonlinear fractional Schrödinger equation with second‐order spatio‐temporal dispersion via double Laplace transform method
Author(s) -
Kaabar Mohammed K. A.,
Martínez Francisco,
GómezAguilar José Francisco,
Ghanbari Behzad,
Kaplan Melike,
Günerhan Hatira
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7476
Subject(s) - mathematics , laplace transform , adomian decomposition method , mathematical analysis , dispersion (optics) , nonlinear system , fractional calculus , derivative (finance) , nonlinear schrödinger equation , conformable matrix , partial differential equation , schrödinger equation , physics , quantum mechanics , financial economics , optics , economics
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.