The Laplace transform of constant proportional Caputo (CPC) derivative is found as [9], for Laplace transform of the derivatives see Table 1: L { 0 C P C D x α h ( x ) } = k 1 ( α ) s + k 0 ( α ) s α L { h ( x ) } − k 0 ( α ) s α − 1 h ( 0 ) .