In this paper we introduce a new multiple-parameters (multi-index) extension of the Wright function that arises from an eigenvalue problem for case hyper-Bessel operator involving Caputo fractional derivatives. We show by giving particular values to parameters involved in special function, leads some known functions (as classical α-Mittag-Leffler Tricomi etc.) on their turn appear as cases so-c...

In this paper, we try to model the dynamics of short term interest rate using the fractional nonhomogeneous differential equation with stochastic free term. This type of equation is similar to one which represents the viscoelastic behavior of certain materials from rheologic point of view. As a final result we obtain the closed formula for prices of zero-coupon bonds. They are analogous to thos...

Transient heat conduction problems are systematically applied to the fading memory formalism with different Mittag-Leffler-type kernels. With such an approach, using various memories naturally results in definitions of fractional operators. Six examples given and interpreted from a common perspective, covering most well-liked versions Mittag-Leffler function. The approach was used as template d...

We introduce the Segal-Bargmann transform associated to Mittag Leffler Fock space and study how it will be connected Fourier transform.We discuss also counterpart of creation annihilation operator in this setting using Caputo Liouville operators. Finally, we give an extension these results case quaternions, particular slice hyperholomorphic setting.

The problem of calculating the Mittag-Leffler function Eρ,μ(z) is considered in paper. To solve this integral representations for are transformed such a way that they could not contain complex variables and parameters. Integral written form allow one to use standard methods numerical integration calculate integrals contained them. verify correctness obtained was calculated both with formulas kn...

Generalization of the integral representation gamma function has been obtained, which shows that Hankel contour assumes rotation in complex plane. The range admissible values for angle is set. Using this representation, generalization Mittag-Leffler obtained expresses value terms integral.

In the framework of Hilbert spaces we shall give necessary and sufficient conditions to define a Dirichlet-to-Neumann operator via Dirichlet principle. Analyzing singular operators, will establish Laurent expansion near singularities as well Mittag–Leffler for related quadratic forms. The established results be exploited solve definitively problem positivity semigroup in Lebesgue spaces. obtain...

In this paper, we investigate two inverse source problems for degenerate time-fractional partial differential equation in rectangular domains. The first problem involves a space-degenerate and the second one time-degenerate equation. Solutions to both are expressed series expansions. For problem, obtained solutions form of Fourier-Legendre series. Convergence uniqueness have been discussed. Fou...