Abstract We consider a general class of integro-differential evolution equations which includes the governing equation generalized grey Brownian motion and time- space-fractional heat equation. present relation between parameters distribution underlying stochastic processes, as well discuss different classes processes providing solutions these equations. For subclass equations, containing Maric...

The focus of this research is to use a new extended beta function and develop the extensions Gauss hypergeometric functions confluent formulas that are presumed be new. Four theorems have also been defined under generalized fractional integral operators provide an image formula for extension functions. Moreover, discussed analogous statements in terms Weyl, Riemann–Liouville, Erdélyi–Kober, Sai...

In this article, a new linear extended multiplier operator is defined utilizing the q-Choi–Saigo–Srivastava and q-derivative. Two generalized subclasses of q—uniformly convex starlike functions order δ—are studied using operator. Necessary conditions are derived for to belong in each two subclasses, subordination theorems involving Hadamard product such particular stated proven. As applications...

This paper is devoted to the study of a new special function, which is called, according to the symbol used to represent this function, as an Aleph function. This function is an extension of the I-function, which itself is a generalization of the well-known and familiar Gand H-functions in one variable. In this paper, a notation and complete definition of the Aleph function will be presented. F...