Numerical approach for fractional integro differential equation systems

In this thesis, numerical solutions of multi-level differential equation systems with fractional Bernoulli collocation method are discussed. Due to the fact that the fractional calculus is applicable to real-life problems, many researchers are working today. The fact that fractional calculus is being studied more recently than classical analysis has also led to too many fractional derivative definitions in literature. In this study, Caputo sense derivative was used for its suitability to the problems. Gamma function, fractional derivative and integral definitions used in solving problems are included. In the third part of the thesis, fractional order linear differential equations, fractional order linear Fredholm integro differential equations, fractional order linear differential equation systems and fractional order linear integro differential equation systems are given to solve them in terms of fractional Bernoulli polynomials. In the fourth section, examples related to the above-mentioned equations are solved, the results obtained are examined with the help of graphics and tables, and it is seen that the method has enough sensitivity. All calculations in this thesis were made with Maple and Matlab programs.