Solution of nonlinear space time fractional differential equations via the fractional projective Riccati expansion method

TL;DR

This paper introduces the fractional projective Riccati expansion method to solve complex nonlinear space-time fractional differential equations, providing new solutions expressed via fractional hyperbolic functions, enhancing understanding of nonlinear physical phenomena.

Contribution

The paper presents a novel fractional projective Riccati expansion method and applies it to obtain new solutions for fractional differential equations, some of which are reported for the first time.

Findings

Solutions expressed in fractional hyperbolic functions.

Application to fractional Burgers and mKdV equations.

Some solutions are novel and first-time results.

Abstract

In this paper, the fractional projective Riccati expansion method is proposed to solve fractional differential equations. To illustrate the effectiveness of the method, we discuss the space-time fractional Burgers equation, the space-time fractional mKdV equation and time fractional biological population model. The solutions are expressed in terms of fractional hyperbolic functions. These solutions are useful to understand the mechanisms of the complicated nonlinear physical phenomena and fractional differential equations. Among these solutions, some are found for the first time. The fractal index for the obtained results is equal to one. Counter examples to compute the fractal index are introduced in appendix.