Generalized caputo fractional derivative and its applications

In 2010, Özarslan and Özergin give an extension of Riemann-Liouville fractional derivative operator with including an extra parameter to the original operator [1]. In this thesis, inspired by the same idea, we introduce an extension of Caputo fractional derivative operator. The extended Caputo fractional derivatives of some elementary functions and some properties of the extended fractional derivative operator are also presented.Keywords: Fractional derivative operator, Hypergeometric functions, Caputo fractional derivative, Mellin transform.