Often referred to as special functions or mathematical functions, the origin of many members
of the remarkably vast family of higher transcendental functions can be traced back to such …

Up to now we have introduced a fractional derivative definition for special simple function
classes. In the following section we will present common generalizations for arbitrary …

We consider an initial value problem for a class of nonlinear fractional differential equations
involving Hilfer fractional derivative. We prove existence and uniqueness of global solutions …

In this paper, we study a certain family of generalized Riemann–Liouville fractional
derivative operators of order α and type β, which were introduced and investigated in …

In this paper we investigate diffusion equations on Cantor space-time and we obtain
approximate solutions by using the local fractional Adomian decomposition method derived …

In this paper, the solution of a fractional diffusion equation with a Hilfer-generalized
Riemann–Liouville time fractional derivative is obtained in terms of Mittag–Leffler-type …

Our main objective in this survey-cum-expository article is essentially to present a review of
some recent developments involving various classes of the Mittag-Leffler type functions …

We introduce the wave equation in fractal vibrating string in the framework of the local
fractional calculus. Our particular attention is devoted to the technique of the local fractional …

In this paper, a two-dimensional conformable fractional wave equation describing a circular
membrane undergoing axisymmetric vibrations is formulated. It was found that the analytical …

We investigate the solution of space–time fractional diffusion equations with a generalized
Riemann–Liouville time fractional derivative and Riesz–Feller space fractional derivative …