## THERMAL SCIENCE

International Scientific Journal

### OPTICAL MODELLING OF THE SPACE-TIME FRACTIONAL ECKHAUS EQUATION

**ABSTRACT**

In this paper, the space-time fractional Eckhaus equation is considered and solved using the a direct method (Khater method) to obtain exact solutions. This method produces more solutions when compared to other known methods. The real solutions of this equation are classified as travelling wave, kink, periodic and solitary wave solutions. These solutions are searched with the help of the fractional conformable derivative sense. Some graphs and tables are drawn to interpret the solutions and method. With the interpretation of the results, it is explained that the method used is a reliable, effective, powerful and easily applicable technique for obtaining the solutions of fractional differential equations classes in many fields.

**KEYWORDS**

PAPER SUBMITTED: 2022-07-11

PAPER REVISED: 2022-07-24

PAPER ACCEPTED: 2022-08-01

PUBLISHED ONLINE: 2023-04-08

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