New Solutions of time-fractional (3+1)-dimensional Schrödinger model with multiple nonlinearities using hybrid approach in Caputo sense - Qayyum, Mubashir; Ahmad, Efaza; Alhefthi, Reem K.; Saeed, Syed Tauseef; İnç, Mustafa (Springer, 2024)
The (3+1)-dimensional Schrodinger model plays an importance role in capturing highly nonlinear optical phenomena with ultra-short pulses. In this regard, the objective of current study is to propose a hybrid approach for the solution of time-fractional sixth order Schrodinger equations in (3 + 1) dimensions with multiple nonlinearities. In this methodology, Laplace transformation is mixed with fractional homotopy perturbation algorithm in Caputo sense for the solution of complex equations. The efficiency of proposed methodology is checked and validated by applying it to different test problems, and by discovering new solutions with better accuracy. Convergence and error estimation are verified theoretically, numerically and graphically. The effect of fractional parameter on wave profiles is studied graphically throughout the fractional domain. Analysis reveals that increase in fractional parameter elevate the real, and decrease the imaginary components of wave profile in current study. The application of proposed algorithm to highly nonlinear fractional models in higher order and dimension clear indicate its validity and competency in the complex scenarios which may arise in various fields of science and engineering.
Keywords: Schrodinger model; Laplace transform; Caputo-fractional derivative; Homotopy perturbation