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 ...

In this work we show that the composition of the integral and derivative operators of order phi, T_phi = D_phi◦I_phi, is a singular integral operator.This result in addition with the results obtained in [HV2] of boundedness ...

In this paper we study inequalities with weights for fractional operators Tαgiven by convolution with a kernel Kαwhich is supposed to satisfy some size condition and a fractional Hörmander type condition. As it is done for ...

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 ...