Stability analysis of distributed order Hilfer-Prabhakar di erential equations

Abstract

In the current study we presented a distributed order form of HilferPrabhakar (DHP) derivative, which in special cases reduces to the existent denitions of fractional or distributed order derivatives. Moreover, we analyzed the stability of DHP dierential equations, which are the generalized form of all previous distributed or fractional dierential equations. The obtained results showed that sucient conditions on asymptotic stability of these systems have been obtained through the generalized properties of Mittag-Leer functions and the Laplace transform. Moreover, a number of conditions on stability analysis of such systems have been introdu