Variable separation for time fractional advection-dispersion equation with initial and boundary conditions

In this pa per, vari able sep a ra tion method com bined with the prop er ties of Mittag-Leffler func tion is used to solve a vari able-co ef fi cient time frac tional advection-dis per sion equa tion with ini tial and bound ary con di tions. As a re sult, a ex plicit ex act so lu tion is ob tained. It is shown that the vari able sep a ra tion method can pro vide a use ful math e mat i cal tool for solv ing the time frac tional heat trans fer equa tions.