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

By Pundikala Veeresha, Doddabhadrappla Gowda Prakasha, Sunil Kumar. Mathematical methods in the applied sciences, 2020

168 citations recorded by the source corpus.

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.

Subfields: Modeling and Simulation, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/ae7a0323b50763f2df22861556027c6b6eea1cb5

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In Modeling and Simulation

1. Behzad Ghanbari
2. Sunil Kumar

In Numerical Analysis

1. Behzad Ghanbari
2. Sunil Kumar

In Statistical and Nonlinear Physics

1. Behzad Ghanbari
2. Sunil Kumar

Citations in the corpus

• A study on fractional predator–prey–pathogen model with Mittag–Leffler kernel‐based operators (2020, methodology): “…Hilbert space method [31, 32], Crank–Nicholson difference method [33], Variational approach [34, 35], q-homotopy analysis method [36], Laplace HPM [37, 36], Numerical schemes [38, 39], fixed point technique [40, 41], predictor–corrector, and spectral scheme [42, 43], the Laplace transform method…”