The paper introduces a new integral operator which generalizes the Prabhakar integral operator. The boundedness on the space of continuous functions and on the space of Lebesgue integrable functions on an interval is ...

In this paper we study an n-dimensional generalization of time-fractional diffusion-wave equation, where the Laplacian operator is replaced by the ultra-hyperbolic operator and the time-fractional derivative is taken in ...

In this paper we study an n-dimensional generalization of timefractional diffusion-wave equation, where the Laplacian operator is replaced by the ultra-hyperbolic operator and the time-fractional derivative is taken in the ...

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have pro- vided solutions of various families ...

Eigenfunctions associated with Riemann–Liouville and Caputo fractional differential operators are obtained by imposing a restriction on the fractional derivative parameter. Those eigenfunctions can be used to express the ...

Given 0 <α< n and a Young function η, we consider the generalized fractional maximal operator Mα,η defined by Mα,η f (x) = sup Bx |B| α/n || f ||η,B, where the supremum is taken over every ball B contained in Rn . In this ...

In this paper we will introduce a new and modi ed Riemann-Liouville fractional operator that resulted from modifying the extended fractional derivative due to M. Ozarslan. We will study some familiar functions regarding ...