After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each oth...

We investigate the well-posedness and asymptotic self-similarity of solutions to a generalized Smoluchowski coagulation equation recently introduced by Bertoin and Le Gall in the context of continuousstate branching theory. In particular, this equation governs the evolution of the Lévy measure of a critical continuous-state branching process which becomes extinct (i.e., is absorbed at zero) alm...

In this paper, generalized versions of Hadamard and Fejér–Hadamard type fractional integral inequalities are obtained. By using integrals containing Mittag-Leffler functions, some well-known results for convex harmonically functions generalized. The paper connected with various published inequalities.

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...

By observing that the fractional Caputo derivative of order α ∈ (0, 1) can be expressed in terms a multiplicative convolution operator, we introduce and study class such operators which also have same self-similarity property as derivative. We proceed by identifying subclass is bijection with set Bernstein functions provide several representations their eigenfunctions, corresponding function, g...

We show that data from recent experiments carried out on the kinetics of DNA escape from alpha-hemolysin nanopores [M. Wiggin, C. Tropini, C. T. Cossa, N. N. Jetha, and A. Marziali, Biophys. J. 95, 5317 (2008)] may be rationalized by a model of chain dynamics based on the anomalous diffusion of a particle moving in a harmonic well in the presence of a delta function sink. The experiments of Wig...