Study on stability analysis of distributed order fractional differential equations with a new approach

Authors

  • Mostafa Eslami Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran
Abstract:

The study of the stability of differential equations without its explicit solution is of particular importance. There are different definitions concerning the stability of the differential equations system, here we will use the definition of the concept of Lyapunov. In this paper, first we investigate stability analysis of distributed order fractional differential equations by using the asymptotic expression of Mittag-Leffler functions, then we check the stability of distributed order fractional differential equations system with the multi-step fractional differential transform method to demonstrate the efficiency and effectiveness of the proposed procedure.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

Stability Analysis of Distributed Order Fractional Differential Equations

and Applied Analysis 3 fractional order to distributed order fractional. In Section 4, we introduce the distributed order fractional evolution systems C doD α t x t A C doD β t x t Bu t , x 0 x0, 0 < β < α ≤ 1, 1.5 where u t is control vector, and generalize the results obtained in Section 3 for this case. Finally, the conclusions are given in the last section. 2. Elementary Definitions and The...

full text

Basic results on distributed order fractional hybrid differential equations with linear perturbations

In this article, we develop the distributed order fractional hybrid differential equations (DOFHDEs) with linear perturbations involving the fractional Riemann-Liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. Furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-Lipschit...

full text

Theory of Hybrid Fractional Differential Equations with Complex Order

We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the exis...

full text

On the stability of linear differential equations of second order

The aim of this paper is to investigate the Hyers-Ulam stability of the  linear differential equation$$y''(x)+alpha y'(x)+beta y(x)=f(x)$$in general case, where $yin C^2[a,b],$  $fin C[a,b]$ and $-infty

full text

basic results on distributed order fractional hybrid differential equations with linear perturbations

in this article, we develop the distributed order fractional hybrid differential equations (dofhdes) with linear perturbations involving the fractional riemann-liouville derivative of order $0 < q < 1$ with respect to a nonnegative density function. furthermore, an existence theorem for the fractional hybrid differential equations of distributed order is proved under the mixed $varphi$-lipschit...

full text

Exponential stability of fractional stochastic differential equations with distributed delay

*Correspondence: [email protected] School of Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013, China Abstract Equations driven by fractional Brownian motion are attracting more and more attention. This paper considers fractional stochastic differential equations with distributed delay. With the variation-of-constants formula, an explicit expression and asymptotic ...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 4  issue 3 (Special issue)

pages  1- 21

publication date 2018-07-01

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023