Wave Soliton Solutions for Conformable-Fractional Partial Differential Equations

The Laplace residual power series technique was previously proposed for solving linear and nonlinear fractional differential equations in the sense of Caputo using independent theories and related expansions. In this research, we focus on modifying this technique to more effectively solve linear and nonlinear fractional partial differential equations within the framework of the conformable fractional derivative. This modification was employed to construct wave soliton solutions for a class of conformable-fractional partial differential equations. Supported by proven theories, new expansions are used to enhance the modified technique. We test the proposed method with four different types of nonlinear time-conformable-fractional partial differential equations. The solutions are shown graphically for various orders of the fractional derivative. We compare the results with the exact solutions in cases of the classical derivative. All results demonstrate the method's simplicity, efficiency, and accuracy.