Stability of fractional-order systems with Prabhakar derivatives

08/09/2020
by   Roberto Garrappa, et al.
0

Fractional derivatives of Prabhakar type are capturing an increasing interest since their ability to describe anomalous relaxation phenomena (in dielectrics and other fields) showing a simultaneous nonlocal and nonlinear behaviour. In this paper we study the asymptotic stability of systems of differential equations with the Prabhakar derivative, providing an exact characterization of the corresponding stability region. Asymptotic expansions (for small and large arguments) of the solution of linear differential equations of Prabhakar type and a numerical method for nonlinear systems are derived. Numerical experiments are hence presented to validate theoretical findings.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

08/10/2019

A comparison between Caputo and Caputo-Fabrizio fractional derivatives for modelling Lotka-Volterra differential equations

In this paper, we apply the concept of the fractional calculus to study ...
10/22/2021

Fractional Modeling in Action: A Survey of Nonlocal Models for Subsurface Transport, Turbulent Flows, and Anomalous Materials

Modeling of phenomena such as anomalous transport via fractional-order d...
08/25/2020

A fractional stochastic theory for interfacial polarization of cell aggregates

We present a theoretical framework to model the electric response of cel...
06/19/2019

On mixed steps-collocation schemes for nonlinear fractional delay differential equations

This research deals with the numerical solution of non-linear fractional...
04/15/2021

Numerical stability of Grünwald-Letnikov method for time fractional delay differential equations

This paper is concerned with the numerical stability of time fractional ...
10/15/2017

A Unified Spectral Method for FPDEs with Two-sided Derivatives; Stability, and Error Analysis

We present the stability and error analysis of the unified Petrov-Galerk...
01/11/2022

Higher order graded mesh scheme for time fractional differential equations

In this article, we propose a higher order approximation to Caputo fract...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.