On certain formulas for the multivariable hypergeometric functions.
On certain subclass of Bazilevič functions.
On conditions for the boundedness of the Weyl fractional integral on weighted spaces
In this paper we give a sufficient condition on the pair of weights for the boundedness of the Weyl fractional integral from into . Under some restrictions on and , this condition is also necessary. Besides, it allows us to show that for any there exist non-trivial weights such that is bounded from into itself, even in the case .
On contraction principle applied to nonlinear fractional differential equations with derivatives of order α ∈ (0,1)
One-term and multi-term fractional differential equations with a basic derivative of order α ∈ (0,1) are solved. The existence and uniqueness of the solution is proved by using the fixed point theorem and the equivalent norms designed for a given value of parameters and function space. The explicit form of the solution obeying the set of initial conditions is given.
On converse theorems of trigonometric approximation in weighted variable exponent Lebesgue spaces.
On Euler methods for Caputo fractional differential equations
Numerical methods for fractional differential equations have specific properties with respect to the ones for ordinary differential equations. The paper discusses Euler methods for Caputo differential equation initial value problem. The common properties of the methods are stated and demonstrated by several numerical experiments. Python codes are available to researchers for numerical simulations.
On fractional derivatives
On fractional differentiation and integration on spaces of homogeneous type.
In this paper we define derivatives of fractional order on spaces of homogeneous type by generalizing a classical formula for the fractional powers of the Laplacean [S1], [S2], [SZ] and introducing suitable quasidistances related to an approximation of the identity. We define integration of fractional order as in [GV] but using quasidistances related to the approximation of the identity mentioned before.We show that these operators act on Lipschitz spaces as in the classical cases. We prove that...
On Fractional Helmholtz Equations
MSC 2010: 26A33, 33E12, 33C60, 35R11In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.
On generalisation of polynomials in complex plane.
On generalizations of the series of Taylor, Lagrange, Laurent and Teixeira.
On Generalized Weyl Fractional q-Integral Operator Involving Generalized Basic Hypergeometric Functions
Mathematics Subject Classification: 33D60, 33D90, 26A33Fractional q-integral operators of generalized Weyl type, involving generalized basic hypergeometric functions and a basic analogue of Fox’s H-function have been investigated. A number of integrals involving various q-functions have been evaluated as applications of the main results.
On Mikusinski's perators of fractional integration
On Minkowski and Hermite-Hadamard integral inequalities via fractional integration.
On molecules and fractional integrals on spaces of homogeneous type with finite measure
In this paper we prove the continuity of fractional integrals acting on nonhomogeneous function spaces defined on spaces of homogeneous type with finite measure. A definition of the molecules which are used in the theory is given. Results are proved for , , BMO, and Lipschitz spaces.
On Multidimensional Analogue of Marchaud Formula for Fractional Riesz-Type Derivatives in Domains in R^n
2000 Mathematics Subject Classification: 26A33, 42B20There is given a generalization of the Marchaud formula for one-dimensional fractional derivatives on an interval (a, b), −∞ < a < b ≤ ∞, to the multidimensional case of functions defined on a region in R^n
On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes
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).
On multiplication formulae for Fox's H-function.
On one class of operators associated with differential equations of fractional order.
On q–Analogues of Caputo Derivative and Mittag–Leffler Function
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.