Numaerical solution of fractional partial differential equations by fractionation

This thesis focuses on obtaining and comparing the solutions of fractional order Burgers' and Korteweg-de Vries (KdV) equations using finite difference and multiquadric radial basis methods in space, and the "Time Splitting Method" in time. Firstly, the historical development of differential equations is examined, and the theoretical foundations of fractional differential equations are detailed. Experimental results have shown that the "Multiquadric Radial Basis Function" method yields more accurate results compared to the "Central Finite Difference" method. The stability of the obtained results was examined and simulated with the help of MATLAB.