Stability analysis of distributed order Hilfer-Prabhakar differential equations

Authors : M MASHOOF, Ah REFAHİ SHEİKHANİ, H SABERİ NAJA

Pages : 299-315

View : 22 | Download : 11

Publication Date : 2018-04-01

Article Type : Research Paper

Abstract :In the current study we presented a distributed order form of Hilfer-Prabhakar insert ignore into journalissuearticles values(DHP); derivative, which in special cases reduces to the existent definitions of fractional or distributed order derivatives. Moreover, we analyzed the stability of DHP differential equations, which are the generalized form of all previous distributed or fractional differential equations. The obtained results showed that sufficient 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 introduced by using a new definition of inertia of a matrix.
Keywords : Distributed order fractional derivative, Hilfer Prabhakar derivative, Asymptotic stability