Non-Markovian processes are widespread in natural and human-made systems, yet explicit modeling and analysis of such systems is underdeveloped. We consider a non-Markovian dynamic network with random link activation and deletion (RLAD) and heavy-tailed Mittag-Leffler distribution for the interevent times. We derive an analytically and computationally tractable system of Kolmogorov-like forward ...

A generalized multivariate problem due to V. M. Zolotarev is considered. Some related results on geometric random sums and (multivariate) stable distributions are extended a more general case of “anisotropic” summation where independent vectors with index having special distribution Anisotropic-geometric introduced. It demonstrated that these coordinate-wise scale mixtures elliptically contoure...

Various extensions of classical gamma, beta, Gauss hypergeometric and confluent functions have been proposed recently by many researchers. In this paper, we further generalized extended beta function with some its properties such as symmetric properties, summation formulas, integral representations, connection other special error, Mittag – Leffler, incomplete hypergeometric, Wright, Fox H Meije...

The objective of this paper is to investigate natural transform Meijer’s G-Function in which Riemann–Liouville integrals are replaced by more general Prabhakar integrals. We analyze and discuss its properties terms Mittag-Leffler functions. Further, we show some applications these classical equations mathematical physics, like the heat free electron laser equations, difference-differential gove...

Pathway idea is a switching mechanism by which one can go from one functional form to another, and to yet another. It is shown that through a parameter α, called the pathway parameter, one can connect generalized type-1 beta family of densities, generalized type-2 beta family of densities, and generalized gamma family of densities, in the scalar as well as the matrix cases, also in the real and...

In the paper, an overview is presented of results on convergence rate bounds in limit theorems concerning geometric random sums and their generalizations to mixed Poisson sums, including case where mixing law itself a exponential distribution. The main focus upper for Zolotarev ζ-metric as distance between pre-limit laws. New are that extend existing estimates (in well-known Rényi theorem) cons...

The main goal of the paper is to use a generalized proportional Riemann–Liouville fractional derivative (GPRLFD) model BAM neural networks and study some stability properties equilibrium. Initially, several GPRLFD are proved, such as squared function. Additionally, comparison results for provided. Two types equilibrium with defined. In connection applied its singularity at initial time, Mittag-...

In this paper, we provide a context for the modeling approaches that have been developed to describe non-Gaussian diffusion behavior, which is ubiquitous in diffusion weighted magnetic resonance imaging of water in biological tissue. Subsequently, we focus on the formalism of the continuous time random walk theory to extract properties of subdiffusion and superdiffusion through novel simplifica...