Quantum mechanics

Korteweg–de Vries equation

Differential equation

Conformable matrix

Applied mathematics

Economics

Physics

Nonlinear system

Mathematics

Mathematical analysis

Ordinary differential equation

Financial economics

First-order partial differential equation

Partial differential equation

Fractional calculus

Derivative (finance)

Computers & Mathematics with Applications

The conformable fractional derivative was proposed by R. Khalil et al. in 2014, which is natural and obeys the Leibniz rule and chain rule. Based on the properties, a class of time-fractional partial differential equations can be reduced into ODEs using traveling wave transformation. Then the simplest equation method is applied to find exact solutions of some time-fractional partial differential equations. The exact solutions (solitary wave solutions, periodic function solutions, rational function solutions) of time-fractional generalized Burgers equation, time-fractional generalized KdV equation, time-fractional generalized Sharma–Tasso–Olver (FSTO) equation and time-fractional fifth-order KdV equation, (3+1)-dimensional time-fractional KdV–Zakharov–Kuznetsov (KdV–ZK) equation are constructed. This method presents a wide applicability to solve some nonlinear time-fractional differential equations with conformable derivative.

Simplest equation method for some time-fractional partial differential equations with conformable derivative