FRACTIONAL ORDER DERIVATIVE AND RELATIONSHIP BETWEEN DERIVATIVE AND COMPLEX FUNCTIONS

The concept of fractional order derivative can be found in widerange of many different areas. Due to this case, there are many methods aboutfractional order derivative (FOD). The most of them are Euler, RiemannLiouville, Grunwald-Letnikov, Oldham-Spanier, Miller-Ross, Kolwankar-Gangal,and Caputo methods which are fractional order derivatives as mentioned in theliterature. However, they are not sound and complete for constant and identityfunctions. This case means that they are curve fitting or curve approximationmethods.FOD concept was defined in [10].The deficiencies of Euler, RiemannLiouville, Grunwald-Letnikov, Oldham-Spanier, Miller-Ross, Kolwankar-Gangal,and Caputo methods were illustrated in this study. In this study, the conceptof FOD and its relationships with complex functions was handled

Keywords:

Derivative, Fractional Order Derivative,

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Inonu University, Department of Computer Engineering, 44280, Malatya / Turkey
E-mail address: ali.karci@inonu.edu.tr, ahmet.karadogan@inonu.edu.tr