Quantum mechanics

Algorithm

Exact solutions in general relativity

Philosophy

Statistics

Variety (cybernetics)

Conformable matrix

Applied mathematics

Computation

Thermodynamics

Physics

Nonlinear system

Mathematics

Duffing equation

Work (physics)

Mathematical analysis

Traveling wave

Reaction–diffusion system

Numerical analysis

Novelty

Theology

Fractional calculus

Results in Physics

In this paper, we obtain the exact traveling solutions of the M-fractional generalized reaction Duffing model and density dependent M-fractional diffusion reaction equation by using three fertile, G′/G,1/G, modified G′/G2 and 1/G′-expansion methods. These methods contribute a variety of exact traveling wave solutions to the scientific literature. The obtained solutions are also verified for the aforesaid equations through symbolic soft computations. Furthermore, some results are explained through numerical simulations that show the novelty of our work. Moreover, we observe that all the solutions are new and an excellent contribution in the existing literature of solitary wave theory.

Exact traveling wave solutions for two prolific conformable M-Fractional differential equations via three diverse approaches