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...

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.

Abstract. In this paper a reliable algorithm for the iterative Laplace transform method (ILTM) is presented. ILTM is a combination of Laplace transform method and Iterative method to solve spaceand timefractional telegraph equations. The fractional derivatives are considered in Caputo sense. Closed form analytical expressions are derived in terms of the Mittag-Leffler functions. An illustrative...

Birgit Mosch,1,4 Markus Morawski,1,3 Anja Mittag,2 Dominik Lenz,2 Attila Tarnok,2 and Thomas Arendt1 1Paul Flechsig Institute of Brain Research, Department of Neuroanatomy, 2Department of Pediatric Cardiology, Cardiac Center Leipzig, and 3Interdisciplinary Center of Clinical Research, Faculty of Medicine, University of Leipzig, D-04109 Leipzig, Germany, and 4Institute of Radiopharmacy, Departme...

We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions. Furthermore, multidimensional extensions of the Bernoulli and Appell polynomials are derived generalizing the relevant generating functions, and using the Hermite-Kampé de Fériet (or Gould-Hopper)...