In this paper, we introduce and study the existence and uniqueness theorem of the solution for the fractional Newell-Whitehead-Segel equation within Caputo-Fabrizio fractional operator. Also, we propose a new numerical method known as natural reduced differential transform method (NRDTM) for solving this equation. We confirm our theoretical discussion with two numerical examples in order to achieve the validity and accuracy of the proposed method. The computations, associated with these examples, are performed by MATLAB software package.
(R1524) The Existence and Uniqueness of Solution for Fractional Newel-Whitehead-Segel Equation within Caputo-Fabrizio Fractional Operator,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 16,
2, Article 7.
Available at: https://digitalcommons.pvamu.edu/aam/vol16/iss2/7