We establish the necessary and sufficient condition for the boundedness of the fractional integral operator  in Morrey space on non-homogeneous quasimetric measure space. Our results can be viewed as Spanne- and Adams-type inequalities for non-homogeneous quasimetric space. Furthermore, we also obtain Olsen-type inequalities involving  Our methods to prove such results also involve about the boundedness of maximal functions in non-homogeneous Morrey spaces. Our results heavily rely on the fact that our underlying spacesare nonempty under some conditions for our functions f. That is, characteristic function of a ball belongs to our underlying spaces.

fractional integral operator, Morrey space, non-homogeneous space, Olsen inequality.