Abstract The Mittag–Leffler function is universally acclaimed as the Queen function of
fractional calculus. The aim of this work is to survey the key results and applications …

The heat equation is parabolic partial differential equation and occurs in the characterization
of diffusion progress. In the present work, a new fractional operator based on the Rabotnov …

This work suggested a new generalized fractional derivative which is producing different
kinds of singular and nonsingular fractional derivatives based on different types of kernels …

This review article aims to stress and reunite some of the analytic formalism of the
anomalous diffusive processes that have succeeded in their description. Also, it has the …

This work is devoted to the time-fractional differential equations with the regularized
Prabhakar derivative and their analytical solutions. We generalize the invariant subspace …

We consider an integral transform introduced by Prabhakar, involving generalised multi-
parameter Mittag-Leffler functions, which can be used to introduce and investigate several …

The computation of the Mittag-Leffler (ML) function with matrix arguments, and some
applications in fractional calculus, are discussed. In general the evaluation of a scalar …

A system of fractional differential equations involving non-singular Mittag-Leffler kernel is
considered. This system is transformed to a type of weakly singular integral equations in …

This endeavour provides a new instance of understanding the velocity of a particle in
Brownian motion, using the Fokker-Plank equation. Our treatment is based on the new …

We define an analogue of the classical Mittag-Leffler function which is applied to two
variables, and establish its basic properties. Using a corresponding single-variable function …