Abstarct: The main topic of the present dissertation is to study the inclusive application of Lie groups and geometry in fractional integro-differential equations‎‎. ‎In this thesis, some types of differential equations of integer and fractional order and fractional integro-differential equation are introduced and also‎, ‎the basic concepts of fractional calculus are stated‎. ‎Next‎, ‎group analysis is extended to the differential equations and after finding symmetries‎, ‎invariant solutions of these equations are ‎founded. ‎It ‎is ‎shown ‎that ‎by ‎using ‎this ‎group ‎analysis‎ ‎Conservation laws of differential equations of integer and fractional order are calculated. These conservation laws lead us to find new solutions baxsed on symmetries. Under some suitable conditions, the infinitesimal criterion of invariance for detecting Lie symmetries of fractional integro-differential equations with fractional derivative in both the Caputo and Riemann–Liouville sense is constructed. Then by using the proved theorem for symmetries, ‎the conservation laws of these equations are ‎abtained‎. For simplicity in computing, the Maple software and its application in finding symmetry groups and the conservation laws of the differential equations of the integer and the fractional order ‎are ‎introduced.‎