On novel analytical solution of time-fractional Schrödinger equation within a hybrid transform. (English) Zbl 1531.35364
Summary: In the present work, an efficient analytical approach that relies on the generalized integral transform coupled with the new iterative transform method is proposed in this research. To determine numerical solutions to time fractional linear/nonlinear Schrödinger equations in the frame of Caputo and Atangana-Baleanu derivatives in the Caputo sense, performed via the aforesaid approach. These nonlinear time fractional Schrödinger equations govern a variety of physical behaviors, involving quantum oscillator motion, lattice vibration, electromagnetic wave propagation, fluid flow, and so on. Besides that, the existence and uniqueness of the solution to the nonlinear model are also constructed. Graphical illustrations report the significance of the projected scheme. The findings show that the offered approach is a valuable tool for examining a diverse plethora of issues for evaluating the nonlinear dynamics of multidimensional systems, and it is more efficient than other known analytical techniques, according to the comparison developed.
MSC:
| 35R11 | Fractional partial differential equations |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
Keywords:
generalized integral transform; new iterative transform method; Schrödinger equation; existence and uniqueness analysisReferences:
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