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The Mittag–Leffler function and its application to the ultra-hyperbolic time-fractional diffusion-wave equation
(Taylor & Francis Ltd, 2016-05)
In this paper we study an n-dimensional generalization of time-fractional diffusion-wave equation, where the Laplacian operator is replaced by the ultra-hyperbolic operator and the time-fractional derivative is taken in ...
SOME REMARKS ON GENERALIZED MITTAG-LEFFLER FUNCTION
(Universidad Católica del Norte, Departamento de Matemáticas, 2009)
Linear fractional differential equations and eigenfunctions of fractional differential operators
(2018-05-01)
Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the ...
Characterizations of the boundedness of generalized fractional maximal functions and related operators in Orlicz spaces
(Wiley VCH Verlag, 2017-01)
Given 0 <α< n and a Young function η, we consider the generalized fractional maximal operator Mα,η defined by Mα,η f (x) = sup Bx |B| α/n || f ||η,B, where the supremum is taken over every ball B contained in Rn . In this ...
Sharp bounds for fractional one-sided operators
(Springer Heidelberg, 2016-11)
In this paper, we characterize the sharp boundedness of the one-sided fractional maximal function for one-weight and two-weight inequalities. Also a new two-weight testing condition for the one-sided fractional maximal ...
Pseudo-fractional differential equations and generalized g-Laplace transform
(2021-09-01)
In this article, we introduce a generalized g-Laplace transform and discuss some essential results of integral transform theory, in particular, involving a ψ-Hilfer pseudo-fractional derivative and function convolution. ...
The obstacle problem for the infinity fractional laplacian
(Springer, 2016-11)
Given g an α-H¨older continuous function defined on the boundary of a bounded domain Ω and given ψ a continuous obstacle defined in Ω, in this article, we find u an α-H¨older extension of g in Ω with u ≥ ψ. This function ...
An alternative definition for the k-Riemann-Liouville fractional derivative
(Hikari Ltd., 2015-01)
The aim of this paper is to introduce an alternative definition for the k-Riemann-Liouville fractional derivative given in [6] and whose advantage is that it is the left inverse of the corresponding of k-RiemannLiouville ...
Hopf lemma for the fractional diffusion operator and its application to a fractional free-boundary problem
(Academic Press Inc Elsevier Science, 2016-02)
We consider a one-dimensional moving-boundary problem for the time-fractional diffusion equation, where the time-fractional derivative of order α. ∈. (0, 1) is taken in the Caputo sense. A generalization of the Hopf lemma ...
Maximal Lp-regularity for fractional differential equations on the line
(Wiley-VCH Verlag, 2017)
© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimWe characterize the Lp -maximal regularity of an abstract fractional differential equation with delay on the Lebesgue spaces. The method is based on the theory of operator-valued ...