Gene

Quantum mechanics

Function (biology)

Transformation (genetics)

Exact solutions in general relativity

Biology

Differential equation

Conformable matrix

Applied mathematics

Elliptic function

Constant coefficients

Biochemistry

Evolutionary biology

Elliptic partial differential equation

Thermodynamics

Physics

Mathematics

Differential (mechanical device)

Mathematical analysis

Chemistry

First-order partial differential equation

Partial differential equation

Fractional calculus

Chinese Journal of Physics

In this paper, we present an approach for seeking exact solutions with coefficient function forms of conformable fractional partial differential equations. By a combination of an under-determined fractional transformation and the Jacobi elliptic equation, exact solutions with coefficient function forms can be obtained for fractional partial differential equations. The innovation point of the present approach lies in two aspects. One is the fractional transformation, which involve the traveling wave transformations used by many articles as special cases. The other is that more general exact solutions with coefficient function forms can be found, and traveling wave solutions with constants coefficients are only special cases of our results. As of applications, we apply this method to the space-time fractional (2+1)-dimensional dispersive long wave equations and the time fractional Bogoyavlenskii equations. As a result, some exact solutions with coefficient function forms for the two equations are successfully found.

A new approach for seeking coefficient function solutions of conformable fractional partial differential equations based on the Jacobi elliptic equation