On the solutions of fractional order integral equtions and integro differential equations

In this thesis, the solution of fractional order integral and integro differential equations with derivatives is given by Conformable Differential Transform Method (CDDM). First, the definition and properties of conformable fractional derivative are introduced, then the basic definitions and theorems required for the method to be used in the thesis are given. As a second step, the Conformable Differential Transform Method (CDDM) and the properties of the method are given. Then, the proposed CDDM in the study is used for the solution of fractional order integral and integro-differential equations, which are very powerful tools for modeling direct natural events and technical systems. The areas of use of integral and integro-differential equations are everywhere where it is necessary to take into account both the past and the current behavior of the system. An algorithm is developed to explain the operation of the proposed CDDM. In order to evaluate the applicability of the method, various numerical examples are examined and the obtained results are compared with the existing methods to show the efficiency of the method. The numerical data obtained revealed that the CDTM approach is promising in solving integral and integro-differential equations.