Results 31 to 40 of about 161,465 (191)

Katugampola Fractional Calculus With Generalized k−Wright Function

European Journal of Mathematical Analysis, 2021
In this article, we present some properties of the Katugampola fractional integrals and derivatives. Also, we study the fractional calculus properties involving Katugampola Fractional integrals and derivatives of generalized k−Wright function nΦkm(z).
Ahmad Y. A. Salamooni, D. D. Pawar
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Fractional integrals and derivatives: mapping properties [PDF]

, 2016
This survey is aimed at the audience of readers interested in the information on mapping properties of various forms of fractional integration operators, including multidimensional ones, in a large scale of various known function spaces.As is well known,
Rafeiro, Humberto, Samko, Stefan
core   +1 more source

Fractional Sums and Differences with Binomial Coefficients

Discrete Dynamics in Nature and Society, 2013
In fractional calculus, there are two approaches to obtain fractional derivatives. The first approach is by iterating the integral and then defining a fractional order by using Cauchy formula to obtain Riemann fractional integrals and derivatives.
Thabet Abdeljawad, Dumitru Baleanu, Fahd Jarad, Ravi P. Agarwal   +3 more
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Fractional Differential Equations with the General Fractional Derivatives of Arbitrary Order in the Riemann–Liouville Sense

Mathematics, 2022
In this paper, we first consider the general fractional derivatives of arbitrary order defined in the Riemann–Liouville sense. In particular, we deduce an explicit form of their null space and prove the second fundamental theorem of fractional calculus ...
Yuri Luchko
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CAUCHY FRACTIONAL DERIVATIVE

Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics", 2020
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.
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Weyl Quantization of Fractional Derivatives

, 2009
The quantum analogs of the derivatives with respect to coordinates q_k and momenta p_k are commutators with operators P_k and $Q_k. We consider quantum analogs of fractional Riemann-Liouville and Liouville derivatives.
Kilbas A. A., Miller K., Oldham K. B., Podlubny I., Samko S. G., Tarasov V. E., Vasily E. Tarasov, Yosida K., Zaslavsky G. M.   +8 more
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Space-time duality for fractional diffusion

, 2009
Zolotarev proved a duality result that relates stable densities with different indices. In this paper, we show how Zolotarev duality leads to some interesting results on fractional diffusion.
Allouba, Baeumer, Becker-Kern, Bertoin, Boris Baeumer, Burdzy, Erkan Nane, Feller, Hille, Lukacs, Mark M. Meerschaert, Meerschaert, Miller, Orsingher, Podlubny, Samko, Samorodnitsky, Scalas, Zolotarev   +18 more
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Deret Maclaurin Turunan Fraksional Fungsi Inverse Trigonometri dan Radius Kekonverganannya

Jambura Journal of Mathematics
Fractional derivatives are a generalization of ordinary derivatives to non-integer or fractional orders. This study presents the fractional derivatives of inverse trigonometric functions (arcsin, arccos, and arctan) with the order constraint 0 α ≤ 1 ...
Siti Miftahurrohmah Khoirunisa, Hafiz Iqbal Anshori, Eka Mulyawati S. Karim   +2 more
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Comparison principles for fractional differential equations with the Caputo derivatives

Advances in Difference Equations, 2018
In this paper, we deal with comparison principles for fractional differential equations involving the Caputo derivatives of order p with 0≤n ...
Ziqiang Lu, Yuanguo Zhu
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FRACTIONAL CENTRAL DIFFERENCES AND DERIVATIVES [PDF]

IFAC Proceedings Volumes, 2006
Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials.
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