## THERMAL SCIENCE

International Scientific Journal

### STRUCTURE OF THE ANALYTIC SOLUTIONS FOR THE COMPLEX NON-LINEAR (2+1)-DIMENSIONAL CONFORMABLE TIME-FRACTIONAL SCHRöDINGER EQUATION

**ABSTRACT**

In this article, the non-linear (2+1)-dimensional conformable time-fractional Schrödinger equation of order α where 0 < α ≤ 1, has been studied within introducing an appropriate fractional traveling wave transformation. The reliable and powerful method, namely the Improved Bernoulli sub equation function method, is applied to investigate some solitary wave, traveling wave and periodic solutions to the aforementioned model which is crucial significance because the model is in the fields of quantum mechanics and energy spectrum. The obtained solutions are new and significant in revealing the pertinent features of the physical phenomenon. Moreover, gotten solutions have been plotted in several kinds, such as in 3-D or 2-D. The impacts of the time evolution are offered in 2-D graphs for visual observation of the properties of the solutions.

**KEYWORDS**

PAPER SUBMITTED: 2022-02-10

PAPER REVISED: 2022-03-24

PAPER ACCEPTED: 2022-04-04

PUBLISHED ONLINE: 2023-04-08

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