Fractional derivatives, non-symmetric and time-dependent Dirichlet forms and the drift form.
Fractional evolution equations governed by coercive differential operators.
Fractional Extensions of Jacobi Polynomials and Gauss Hypergeometric Function
2000 Mathematics Subject Classification: 26A33, 33C45This paper refers to a fractional order generalization of the classical Jacobi polynomials. Rodrigues’ type representation formula of fractional order is considered. By means of the Riemann–Liouville operator of fractional calculus fractional Jacobi functions are defined, some of their properties are given and compared with the corresponding properties of the classical Jacobi polynomials. These functions appear as a special case of a fractional Gauss...
Fractional flux and non-normal diffusion.
Fractional hold circuits versus positive realness of discrete transfer functions.
Fractional integral operators on with Morrey-Campanato norms
We introduce function spaces with Morrey-Campanato norms, which unify , and Morrey-Campanato spaces, and prove the boundedness of the fractional integral operator on these spaces.
Fractional integrals and differentials of variable order in Hölder spaces .
Fractional integrals on spaces of homogeneous type
Fractional integration and fractional differentiation for Jacobi expansions.
Fractional Integration and Fractional Differentiation of the M-Series
Mathematics Subject Classification: 26A33, 33C60, 44A15In this paper a new special function called as M-series is introduced. This series is a particular case of the H-function of Inayat-Hussain. The M-series is interesting because the pFq -hypergeometric function and the Mittag-Leffler function follow as its particular cases, and these functions have recently found essential applications in solving problems in physics, biology, engineering and applied sciences. Let us note that the Mittag-Leffler ...
Fractional Integration of the Product of Bessel Functions of the First Kind
Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for the product of cosine...
Fractional integration on the space and its dual
Fractional integration operator of variable order in the Hölder spaces .
Fractional integro-differentiation in harmonic mixed norm spaces on a half-space
In this paper some embedding theorems related to fractional integration and differentiation in harmonic mixed norm spaces on the half-space are established. We prove that mixed norm is equivalent to a “fractional derivative norm” and that harmonic conjugation is bounded in for the range , . As an application of the above, we give a characterization of by means of an integral representation with the use of Besov spaces.
Fractional integrodifferentiation in Hölder classes of arbitrary order.
Fractional Iteration and a Generalised Abel's Equation in Two Variables
Fractional order calculus: basic concepts and engineering applications.
Fractional order impulsive partial hyperbolic differential inclusions with variable times
This paper deals with the existence of solutions to some classes of partial impulsive hyperbolic differential inclusions with variable times involving the Caputo fractional derivative. Our works will be considered by using the nonlinear alternative of Leray-Schauder type.
Fractional Poisson processes and related planar random motions.
Fractional powers of non-negative operators in Fréchet spaces.