The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.In this paper the multi-dimensional analog of the Gillis-Weiss random walk model is studied. The convergence of this random walk to a fractional diffusion process governed by a symmetric operator defined as a hypersingular integral or the inverse of the Riesz potential in the sense of distributions is proved.* Supported by German Academic Exchange Service (DAAD).
Mathematics Subject Classification: 33D60, 33E12, 26A33Based on the fractional q–integral with the parametric lower limit of
integration, we consider the fractional q–derivative of Caputo type.
Especially, its applications to q-exponential functions allow us to introduce
q–analogues of the Mittag–Leffler function. Vice versa, those functions can
be used for defining generalized operators in fractional q–calculus.
We introduce Sobolev spaces for 1 < p < ∞ and small positive α on spaces of homogeneous type as the classes of functions f in with fractional derivative of order α, , as introduced in [2], in . We show that for small α, coincides with the continuous version of the Triebel-Lizorkin space as defined by Y. S. Han and E. T. Sawyer in [4]. To prove this result we give a more general definition of ε-families of operators on spaces of homogeneous type, in which the identity operator is...
We give some subordination results for new classes of normalized analytic functions containing differential operator of non-Bazilevič type in the open unit disk. By using Jack's lemma, sufficient conditions for this type of operator are also discussed.
The purpose of this paper is to give a characterization of the closure of the Lizorkin space in spaces of Beppo Levi type. As preparations for the proof, we establish the invariance of the Lizorkin space, and give local integral representations for smooth functions.
Mathematics Subject Classification: 26A33In the process of constructing empirical mathematical models of physical phenomena using the fractional calculus, investigators are usually faced with the choice of which definition of the fractional derivative to use, the
Riemann-Liouville definition or the Caputo definition. This investigation
presents the case that, with some minimal restrictions, the two definitions
produce completely equivalent mathematical models of the linear viscoelastic phenomenon....
2000 Mathematics Subject Classification: 26A33, 33C20This paper is devoted to further development of important case of
Wright’s hypergeometric function and its applications to the generalization
of Γ-, B-, ψ-, ζ-, Volterra functions.
In this paper, we develop the approach and techniques of [Boucherif A., Precup R., Semilinear evolution equations with nonlocal initial conditions, Dynam. Systems Appl., 2007, 16(3), 507–516], [Zhou Y., Jiao F., Nonlocal Cauchy problem for fractional evolution equations, Nonlinar Anal. Real World Appl., 2010, 11(5), 4465–4475] to deal with nonlocal Cauchy problem for semilinear fractional order evolution equations. We present two new sufficient conditions on existence of mild solutions. The first...
MSC 2010: 26A33, 44A45, 44A40, 65J10We consider a linear system of differential equations with fractional derivatives, and its corresponding system in the field of Mikusiński operators, written in a matrix form, by using the connection between the fractional and the Mikusiński calculus. The exact and the approximate operational solution of the corresponding matrix equations, with operator entries are determined, and their characters are analyzed. By using the packages Scientific Work place and...
2000 Mathematics Subject Classification: 33D60, 26A33, 33C60The present paper envisages the applications of Riemann-Liouville fractional q-integral operator to a basic analogue of Fox H-function. Results involving the basic hypergeometric functions like Gq(.), Jv(x; q), Yv(x; q),Kv(x; q), Hv(x; q) and various other q-elementary functions associated with the Riemann-Liouville fractional q-integral operator have been deduced as special cases of the main result.
Currently displaying 21 –
40 of
48