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 asympto...

The theory of derivatives and integrals of fractional in fractional calculus have found enormousapplications in mathematics, physics and engineering so for that reason we need an efficient and accurate computational method for the solution of fractional differential equations. This paper presents a numerical method for solving a class of linear and nonlinear multi-order fractional differential ...

In this paper the multi-dimensional random walk models governed by distributed fractional order differential equations and multi-term fractional order differential equations are constructed. The scaling limits of these random walks to a diffusion process in the sense of distributions is proved. Simulations based upon multi-term fractional order differential equations are performed. Mathematics ...

In this paper we propose a relatively new semi-analytical technique to approximate the solution of nonlinear multi-order fractional differential equations (FDEs). We present some results concerning to the uniqueness of solution of nonlinear multi-order FDEs and discuss the existence of solution for nonlinear multi-order FDEs in reproducing kernel Hilbert space (RKHS). We further give an error a...

In this paper, the finite-time stabilization of a class of multi-state time delay of fractional-order system is proposed.First, we define finite-time stability with the fractional-order system.Second,by using Generalized Gronwall’s approach and the methods of the inequality,we get some conditions of finite-time stability for the fractional system with multi-state delay.Finally,a numerical examp...

An extension of the general fractional calculus (GFC) an arbitrary order, proposed by Luchko, is formulated. This also based on a multi-kernel approach, in which Laplace convolutions different Sonin kernels are used. The GFC order considered for case intervals (a,b) where ??<a<b??. Examples operators orders proposed.