A fractional model for propagation of classical optical solitons by using nonsingular derivative

• Published in: Mathematical methods in the applied sciences Vol. 47; no. 13; pp. 10609 - 10623
• Main Authors: Veeresha, P., Prakasha, D. G., Kumar, Sunil
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 15.09.2024
• Subjects: Atangana‐Baleanu fractional derivative; Fractional calculus; generalized nonlinear Schrödinger equation; Homotopy theory; Laplace transform; Mechanical properties; Mechanical systems; q‐homotopy analysis method; Schrodinger equation; Solitary waves
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.6335

The Schrödinger equation depends on the physical circumstance, which describes the state function of a quantum‐mechanical system and gives a characterization of a system evolving with time. The essential focus of proposed research is to observe the solution for fractional generalized nonlinear Schrödinger (FGNS) equation using q‐homotopy analysis transform method ( q‐HATM). The fractional order derivative is taken in the Atangana‐Baleanu (AB) sense. The physical behaviours of achieved solution for FGNS equation are discussed and sketch out graphically. The existence of the solution for the FGNS equation is presented through theorems 4.1 to 4.3. The proposed numerical simulations confirm the advantages of the AB derivative through q‐HATM. Few numerical experiments were carried out to validate the proposed method. Moreover, numerical simulations are carried out to verify efficiency and robustness of the derived results by considering two cases.