This thesis is a study of inverse problems in fractional calculus where two major theorems of existence and uniqueness for the solution of fractional order integro differential equations have been proved in different approaches. Delay fractional order integro differential equations have also been discussed; some related results have been achieved. Also, three methods for solving inverse problems of fractional order integro differential equations with and without delay have been improved. These methods were illustrated by some examples. Some applications of problems associated with fractional...