A novel method of an optimal summation is developed that allows for calculating from small-variable asymptotic expansions the characteristic amplitudes variables tending to infinity. The in two versions, as self-similar Borel–Leroy or Mittag–Leffler summations. It based on optimized iterated roots approximants applied and Mittag–Leffler- transformed series with subsequent inverse transformation...

The asymptotic stable region and long-time decay rate of solutions to linear homogeneous Caputo time fractional ordinary differential equations (F-ODEs) are known be completely determined by the eigenvalues coefficient matrix. Very different from exponential classical ODEs, F-ODEs only polynomially, leading so-called Mittag-Leffler stability, which was already extended semi-linear with small pe...

In this paper a closed form solution of a fractional integro-differential equation of Volterra type involving Mittag-Leffler function has been obtained using straight forward technique of Sumudu transform. Some particular cases have also been considered.

In this paper, we apply the well-known aggregation mappings on Mittag-Leffler-type functions to investigating new approximation error estimates of a W-Hilfer fractional differential equation, by different concept Ulam-type stability in both bounded and unbounded domains.

We consider the stochastic fixed point equation Xn d = Xn−D +B that appears in several applications, for example in the Bolthausen-Sznitman coalescent or in the analysis or recursive algorithms. In this paper we provide a systematic study on these kinds of stochastic fixed point equations. It turns out that depending on the singularity structure of the the moment generating function of D the li...

We investigate the asymptotic behaviour of the Mittag-Leffler polynomials Gn(z) for large n and z , where z is a complex variable satisfying 0 arg z 2 π . A summary of the asymptotic properties of Gn(ix) for real values of x and an approximation for its extreme zeros as n→∞ are given. When the variables are such that z/n is finite, an expansion is obtained using the method of steepest descents ...

In this paper, we present an integrodifferential diffusion equation for continuous-time random walk that is valid for a generic waiting time probability density function. Using this equation, we also study diffusion behaviors for a couple of specific waiting time probability density functions such as exponential and a combination of power law and generalized Mittag-Leffler function. We show tha...

In this article, we extend fractional operators with nonsingular Mittag-Leffler kernels, a study initiated recently by Atangana and Baleanu, from order [Formula: see text] to higher arbitrary order and we formulate their correspondent integral operators. We prove existence and uniqueness theorems for the Caputo ([Formula: see text]) and Riemann ([Formula: see text]) type initial value problems ...