The numerical solutions of conformable fractional solute transport problem with a new numerical method

This thesis consists of five main sections. In the first section, a general literature review on the concept of fractional derivative is included. In the second section, the basic definitions and theorems used in the study are presented. In the third section, the proposed new numerical method is introduced in detail. In the fourth section, the conformable fractional two-dimensional solute transport problem (CFTDSTP) is solved numerically using the conformable fractional q-formable homotopy analysis transform method (CFqFHADM) and various numerical simulations are performed in order to reveal the effectiveness and reliability of the solutions obtained with this method. In addition, the accuracy of the method is analyzed by comparing the obtained numerical solutions with the existing analytical solutions. In the last section, it is emphasized that the proposed method can be used as a simple, powerful and effective tool in solving nonlinear compatible fractional differential equations.