Document Type : Research Paper

**Author**

Department of Mathematics, Takestan branch, Islamic Azad University, Takestan, Iran

**Abstract**

In the present paper, modified simple equation method (MSEM) is implemented for obtaining exact solutions of three nonlinear (3 + 1)-dimensional space-time fractional equation, namely three types of modified Korteweg-de-Vries (mKdV) equations. Here, the derivatives are of the type of conformable fractional derivatives. The solving process produces a system of algebraic equations which is possible to be easily with no need of using software for determining unknown coefficients. Results show that this method can supply a powerful mathematical tool to construct exact solutions of mKdV equations and it can be employed for other nonlinear (3 + 1) - dimensional space-time fractional equations.

**Keywords**

- Modified simple equation method (MSEM)
- Exact solutions
- ( 3 + 1 )- Dimensional fractional equations
- Conformable fractional derivative

**Main Subjects**

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March 2024

Pages 413-424

**Receive Date:**04 June 2022**Revise Date:**27 April 2023**Accept Date:**28 September 2023