Conformable fractional wave equation and conformable fractional KdV equation from the ordinary Newton equation with deformed translational symmetry

Abstract

In this paper, we derive the conformable fractional wave equation and conformable fractional KdV equation from the ordinary Newton equation with deformed translational symmetry. At first, we obtain a solution to the dimensionless 1D conformable wave equation with fixed ends, and then we study the D'Alembert solution for full space. Next, we examine the dimensionless 2D conformable fractional wave equation in the deformed disk. Finally, we derive the conformable fractional KdV equation and explore its solution.