Approximate Analytical Solutions of Time-Fractional Modified Cortège De-Vries (M-Kdv) Equation Using Conformable Fractional Reduced Differential Transform Method

Abstract

In this thesis, the conformable fractional reduced differential transform method (CFRDTM) is proposed as an effective approach for obtaining approximate analytical solutions to time fractional m-KdV equations. CFRDTM combines two powerful techniques: the Conformable Fractional Calculus which helps to accurately model how things change over time in a way that better reflects how they actually behave in the real world and the Reduced Differential Transformation Method which simplifies the problem by turning the complex original equation into a series of much easier algebraic equations. Application of the scheme is illustrated on time fractional m-KdV equations to obtain approximation analytical solutions. The convergence of these solutions has been rigorously analyzed and compared with the existing methods including the homotopy perturbation transform method. Two representative examples are used to illustrate the effectiveness and accuracy of the method. From this we have observed that our result is in a good agreement with results found in the existing literature.