CAUCHY FRACTIONAL DERIVATIVE
Copyright policy )CAUCHY FRACTIONAL DERIVATIVE
In this paper, we introduce a new sort of fractional derivative. For this, we consider the Cauchy's integral formula for derivatives and modify it by using Laplace transform. So, we obtain the fractional derivative formula F(α)(s) = L{(–1)(α)L–1{F(s)}}. Also, we find a relation between Weyl's fractional derivative and the formula above. Finally, we give some examples for fractional derivative of some elementary functions.
- Bitlis Eren University Turkey
- South Ural State University (Южно-Уральский государственный университет) Russian Federation
- Bitlis Eren University Turkey
преобразование Лапласа, Fractional derivatives and integrals, Laplace transform, Cauchy's integral formula for derivatives, интегральная формула Коши для производных, дробная производная Вейля, дробное исчисление, fractional calculus, Weyl's fractional derivative, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Weyl's fractional derivative fractional calculus Laplace transform Cauchy's integral formula for derivatives
преобразование Лапласа, Fractional derivatives and integrals, Laplace transform, Cauchy's integral formula for derivatives, интегральная формула Коши для производных, дробная производная Вейля, дробное исчисление, fractional calculus, Weyl's fractional derivative, Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane, Weyl's fractional derivative fractional calculus Laplace transform Cauchy's integral formula for derivatives
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