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.
