WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article On the generalized fractional derivatives and their Caputo modification(INT Scientific Research Publications, 2017) Jarad, Fahd; Abdeljawad, Thabet; Baleanu, DumitruIn this manuscript, we define the generalized fractional derivative on AC(gamma)(n) [a, b], the space of functions defined on [a, b] such that gamma(n-1) f is an element of AC [a, b], where gamma = x(1-rho) d/dx. We present some of the properties of generalized fractional derivatives of these functions and then we define their Caputo version.Article On a new class of fractional operators(Springeropen, 2017) Jarad, Fahd; Uğurlu, Ekin; Abdeljawad, Thabet; Baleanu, DumitruThis manuscript is based on the standard fractional calculus iteration procedure on conformable derivatives. We introduce new fractional integration and differentiation operators. We define spaces and present some theorems related to these operators.Article On fractional derivatives with generalized Mittag-Leffler kernels(Pushpa Publishing House, 2018) Abdeljawad, Thabet; Baleanu, DumitruFractional derivatives with three parameter generalized Mittag-Leffler kernels and their properties are studied. The corresponding integral operators are obtained with the help of Laplace transforms. The action of the presented fractional integrals on the Caputo and Riemann type derivatives with three parameter Mittag-Leffler kernels is analyzed. Integration by parts formulas in the sense of Riemann and Caputo are proved and then used to formulate the fractional Euler-Lagrange equations with an illustrative example. Certain nonconstant functions whose fractional derivatives are zero are determined as well.