scholarly journals WEYL FRACTIONAL DERIVATIVE OF THE PRODUCT MULTIVARIABLES POLYNOMIALS AND I –FUNCTION.

2017 ◽  
Vol 5 (2) ◽  
pp. 1576-1581
Author(s):  
HarishKumar Mishra. ◽  
Keyword(s):  
Fractional Derivative ◽  
Weyl Fractional Derivative

scholarly journals Fractional calculus of periodic distributions

2011 ◽  
Vol 14 (2) ◽  
Author(s):  
Khaula Khan ◽  
Wilson Lamb ◽  
Adam McBride
Keyword(s):  
Fourier Series ◽  
Fractional Derivative ◽  
Fractional Derivatives ◽  
Arbitrary Order ◽  
Fractional Diffusion ◽  
Difference Quotient ◽  
Fractional Difference ◽  
Periodic Distribution ◽  
Weyl Fractional Derivative ◽  
Derivatives Of

AbstractTwo approaches for defining fractional derivatives of periodic distributions are presented. The first is a distributional version of the Weyl fractional derivative in which a derivative of arbitrary order of a periodic distribution is defined via Fourier series. The second is based on the Grünwald-Letnikov formula for defining a fractional derivative as a limit of a fractional difference quotient. The equivalence of the two approaches is established and an application to a fractional diffusion equation, posed in a space of periodic distributions, is also discussed.

scholarly journals Reflection properties of zeta related functions in terms of fractional derivatives

2020 ◽  
Vol 23 (2) ◽  
pp. 520-533
Author(s):  
Erasmo M. Ferreira ◽  
Anderson K. Kohara ◽  
Javier Sesma
Keyword(s):  
Fractional Derivative ◽  
Zeta Function ◽  
Fractional Derivatives ◽  
Hurwitz Zeta Function ◽  
Integer Order ◽  
Reflection Property ◽  
Complex Order ◽  
Weyl Fractional Derivative ◽  
Ordinary Derivative ◽  
Natural Way

AbstractWe prove that the Weyl fractional derivative is a useful instrument to express certain properties of the zeta related functions. Specifically, we show that a known reflection property of the Hurwitz zeta function ζ(n, a) of integer first argument can be extended to the more general case of ζ(s, a), with complex s, by replacement of the ordinary derivative of integer order by Weyl fractional derivative of complex order. Besides, ζ(s, a) with ℜ(s) > 2 is essentially the Weyl (s − 2)-derivative of ζ(2, a). These properties of the Hurwitz zeta function can be immediately transferred to a family of polygamma functions of complex order defined in a natural way. Finally, we discuss the generalization of a recently unveiled reflection property of the Lerch’s transcendent.

MIXED FRACTIONAL DIFFERENTIATION OPERATORS IN HÖLDER SPACES DEFINED BY USUAL HÖLDER CONDITION

2019 ◽  
Author(s):  
T. Mamatov ◽  
R. Sabirova ◽  
D. Barakaev
Keyword(s):  
Fractional Derivative ◽  
Fractional Differentiation ◽  
Hölder Condition ◽  
Hölder Spaces ◽  
Main Interest ◽  
Hölder Class ◽  
Holder Class ◽  
Function Of Two Variables ◽  
Holder Spaces

We study mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The main interest being in the evaluation of the latter for the mixed fractional derivative in the cases Hölder class defined by usual Hölder condition

scholarly journals A remark on local fractional calculus and ordinary derivatives

2016 ◽  
Vol 14 (1) ◽  
pp. 1122-1124 ◽  
Author(s):  
Ricardo Almeida ◽  
Małgorzata Guzowska ◽  
Tatiana Odzijewicz
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivative ◽  
Short Note ◽  
General Definition ◽  
Local Fractional Derivative ◽  
Fundamental Properties ◽  
Local Fractional Calculus ◽  
Definition Of

AbstractIn this short note we present a new general definition of local fractional derivative, that depends on an unknown kernel. For some appropriate choices of the kernel we obtain some known cases. We establish a relation between this new concept and ordinary differentiation. Using such formula, most of the fundamental properties of the fractional derivative can be derived directly.

On Finite Part Integrals and Hadamard-Type Fractional Derivatives

2018 ◽  
Vol 13 (9) ◽  
Author(s):  
Li Ma ◽  
Changpin Li
Keyword(s):  
Fractional Derivative ◽  
Singular Integral ◽  
Fractional Derivatives ◽  
Continuous Functions ◽  
Finite Part ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Fundamental Properties ◽  
Logarithmic Series ◽  
The Right

This paper is devoted to investigating the relation between Hadamard-type fractional derivatives and finite part integrals in Hadamard sense; that is to say, the Hadamard-type fractional derivative of a given function can be expressed by the finite part integral of a strongly singular integral, which actually does not exist. Besides, our results also cover some fundamental properties on absolutely continuous functions, and the logarithmic series expansion formulas at the right end point of interval for functions in certain absolutely continuous spaces.

Sign in / Sign up

Export Citation Format

Share Document