Table 1 Comparison of the current work with recent studies on the space-time fractional modified third-order KdV Eq. (31).

Current Study

The Auxiliary Equation Method

Diverse soliton solutions (dark, bright, periodic singular, singular, periodic, combined dark-singular, exponential nature, and many other solitary waves);

Sahoo, and Ray⁶⁴

Two integration schemes (the \((\frac{G'}{G})\)-expansion method and the improved \((\frac{G'}{G})\)-expansion method)

Solitary wave solutions only

Rehman et al.⁶⁵

Sardar sub-equation method

bright, dark, singular, periodic singular, combined bright-dark and combined dark-singular soliton solutions

Nazari⁶⁶

modified \((G'/G)\)-expansion method

Singular solutions