In this paper, we are presenting our work where the noninteger order partial differential equation is studied analytically and numerically using the noninteger power series technique, proposed to solve a noninteger differential equation. We are familiar with a coupled system of the nonlinear partial differential equation (NLPDE). Noninteger derivatives are considered in the Caputo operator. The fractional-order power series technique for finding the nonlinear fractional-order partial differential equation is found to be relatively simple in implementation with an application of the direct power series method. We obtained the solution of nonlinear dispersive equations which are used in electromagnetic and optics signal transformation. The proposed approach of using the noninteger power series technique appears to have a good chance of lowering the computational cost of solving such problems significantly. How to paradigm an initial representation plays an important role in the subsequent process, and a few examples are provided to clarify the initial solution collection.
A Truncation Method for Solving the Time-Fractional Benjamin-Ono Equation