The numerical solutions of fractional differential-algebraic equtions by complex transform method

In this thesis, firstly fractional derivative and fractional integral, Riemann-Liouville fractional derivative and integral, Caputo fractional derivative and integral concept is studied and then fractional differential equation, system of fractional differential equation concepts is given. Next, method for analytical and numerical solutions of the fractional differential equations is investigated. This method is complex transform method. The numerical solutions of fractional differential equations, fractional differential equations system and fractional differential-algebraic equations are obtained by this method with the help of various examples, we study to show that these methods are effective and efficient. Keywords: Riemann-Liouville fractional derivative, Fractional differential equation, System of fractional differential equations, Complex transform method, Differential- algebraic equations, Fractional algebraic-differential equation.