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.

We present a new numerical approach to solving the fractional differential Riccati equations numerically. The approach—called Mittag-Leffler–Galerkin method—comprises finite Mittag-Leffler function and Galerkin method. error analysis of method was studied. As result, we two theorems by which can be bounded. In addition analysis, residual correction method, allows us estimate obtain approximate ...

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...

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)...

Abstract We show the asymptotic long-time equivalence of a generic power law waiting time distribution to the Mittag-Leffler waiting time distribution, characteristic for a time fractional continuous time random walk. This asymptotic equivalence is effected by a combination of “rescaling” time and “respeeding” the relevant renewal process followed by a passage to a limit for which we need a sui...