Semi-analytical solutions of conformable fractional partial differential equations

In this study, semi-analytical solutions of conformable fractional partial differential equations, which are expressed with the definition of conformable fractional derivative, which has recently entered the literature, have been investigated. The method used to reach these solutions is the form of the differential transform method, which exists in the literature, adapted to conformable fractional partial differential equations. This derivative-based method aims to find the coefficients of the solution in the Taylor series form. The performance of the method has been tested on a conformable fractional partial equation and a conformable fractional partial equation system. The general operation of the method is to find the transformed form of each term in the differential equation according to the method. Therefore, in the first example, the conformable fractional partial differential equation was designed as an inverse problem with the desire to be an equation containing less common terms in the literature. The conformable fractional partial differential equation system in the other example is an equation system that models a known biochemical process in the literature and has a strong nonlinear term. The results obtained showed that the method stands out due to its ease of application and coding.