Finite-time stability of nonlinear stochastic $ \psi $-Hilfer fractional systems with time delay

In this paper, we study the finite time stability of stochastic $ \psi $-Hilfer fractional-order time-delay systems. Under the stochastic analysis techniques and the generalized Gronwall's inequality for $ \psi $-fractional derivative, the criterion of finite time stability of the solution for nonlinear stochastic $ \psi $-Hilfer fractional systems with time delay is obtained. An example is provided to illustrate the effectiveness of the proposed methods. Some known results in the literature are extended.

[1]  Y. Liu,et al.  Stabilization of stochastic highly non-linear multi-links systems via aperiodically intermittent control , 2022, Autom..

[2]  Chao Wei.  Parameter estimation for partially observed stochastic differential equations driven by fractional Brownian motion , 2022, AIMS Mathematics.

[3]  D. Baleanu,et al.  Finite-time stability of linear stochastic fractional-order systems with time delay , 2021, Advances in Difference Equations.

[4]  Mohammed S Abdo,et al.  Explicit iteration and unique solution for $ \phi $-Hilfer type fractional Langevin equations , 2021, AIMS Mathematics.

[5]  Sotiris K. Ntouyas,et al.  Existence and stability results for $ \psi $-Hilfer fractional integro-differential equation with mixed nonlocal boundary conditions , 2021 .

[6]  X. Shu,et al.  The existence and Hyers-Ulam stability of solution for almost periodical fractional stochastic differential equation with fBm , 2020 .

[7]  Jun-Guo Lu,et al.  Finite-time stability of neutral fractional order time delay systems with Lipschitz nonlinearities , 2020, Appl. Math. Comput..

[8]  Apassara Suechoei,et al.  Existence uniqueness and stability of mild solutions for semilinear ψ-Caputo fractional evolution equations , 2020, Advances in Difference Equations.

[9]  K. Shah,et al.  On the Novel Ulam–Hyers Stability for a Class of Nonlinear $$\psi $$-Hilfer Fractional Differential Equation with Time-Varying Delays , 2019, Mediterranean Journal of Mathematics.

[10]  Xiaodi Li,et al.  Lyapunov conditions for finite-time stability of time-varying time-delay systems , 2019, Autom..

[11]  J. Sousa,et al.  A Gronwall inequality and the Cauchy-type problem by means of ψ-Hilfer operator , 2017, Differential Equations & Applications.

[12]  D. S. Oliveira,et al.  Hilfer–Katugampola fractional derivatives , 2018 .

[13]  N. Derbel,et al.  On Observer Design for Nonlinear Caputo Fractional‐Order Systems , 2018 .

[14]  JinRong Wang,et al.  Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations , 2018, Appl. Math. Comput..

[15]  J. Vanterler da C. Sousa,et al.  On the ψ-Hilfer fractional derivative , 2017, Commun. Nonlinear Sci. Numer. Simul..

[16]  R. Almeida.  A Gronwall inequality for a general Caputo fractional operator , 2017, 1705.10079.

[17]  Omar Naifar,et al.  Comments on "Mittag-Leffler stability of fractional order nonlinear dynamic systems [Automatica 45(8) (2009) 1965-1969]" , 2017, Autom..

[18]  Yong Wu,et al.  The existence and uniqueness theorem of the solution to a class of nonlinear fractional order system with time delay , 2016, Appl. Math. Lett..

[19]  Qixiang Dong,et al.  Weighted fractional differential equations with infinite delay in Banach spaces , 2016 .

[20]  Yang Liu,et al.  Finite time stability of nonlinear impulsive systems and its applications in sampled-data systems. , 2015, ISA transactions.

[21]  P. Balasubramaniam,et al.  Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi's function , 2015, Appl. Math. Comput..

[22]  Liping Chen,et al.  Finite-time stability of fractional delayed neural networks , 2015, Neurocomputing.

[23]  Le Van Hien,et al.  Finite-time stability of a class of non-autonomous neural networks with heterogeneous proportional delays , 2015, Appl. Math. Comput..

[24]  Shi-you Lin.  Generalized Gronwall inequalities and their applications to fractional differential equations , 2013 .

[25]  Aleksandar M. Spasic,et al.  Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach , 2009, Math. Comput. Model..

[26]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .