A survey on the stability of fractional differential equations: Dedicated to Prof. YS Chen on the Occasion of his 80th Birthday

CP Li, FR Zhang - The European Physical Journal Special Topics, 2011 - Springer
Recently, fractional calculus has attracted much attention since it plays an important role in
many fields of science and engineering. Especially, the study on stability of fractional …

[KNYGA][B] Functional fractional calculus

S Das - 2011 - Springer
When a new extraordinary and outstanding theory is stated, it has to face criticism and
skeptism, because it is beyond the usual concept. The fractional calculus though not new …

Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations

M Li, JR Wang - Applied Mathematics and Computation, 2018 - Elsevier
In this paper, we introduce a concept of delayed two parameters Mittag-Leffler type matrix
function, which is an extension of the classical Mittag-Leffler matrix function. With the help of …

[HTML][HTML] Existence results for a coupled system of nonlinear fractional differential equations with three-point boundary conditions

B Ahmad, JJ Nieto - Computers & Mathematics with Applications, 2009 - Elsevier
This paper studies a coupled system of nonlinear fractional differential equations with three-
point boundary conditions. Applying the Schauder fixed point theorem, an existence result is …

[HTML][HTML] LMI stability conditions for fractional order systems

J Sabatier, M Moze, C Farges - Computers & Mathematics with Applications, 2010 - Elsevier
After an overview of the results dedicated to stability analysis of systems described by
differential equations involving fractional derivatives, also denoted fractional order systems …

[HTML][HTML] Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach

MP Lazarević, AM Spasić - Mathematical and Computer Modelling, 2009 - Elsevier
In this paper, a stability test procedure is proposed for linear nonhomogeneous fractional
order systems with a pure time delay. Some basic results from the area of finite time and …

[HTML][HTML] A fractional-order differential equation model of HIV infection of CD4+ T-cells

Y Ding, H Ye - Mathematical and Computer Modelling, 2009 - Elsevier
In this paper, we introduce fractional-order into a model of HIV infection of CD4+ T-cells. We
show that the model established in this paper possesses non-negative solutions, as desired …

[PDF][PDF] Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions

B Ahmad, JJ Nieto - Boundary value problems, 2009 - Springer
This paper deals with some existence results for a boundary value problem involving a
nonlinear integrodifferential equation of fractional order with integral boundary conditions …

Finite-time stability of delayed memristor-based fractional-order neural networks

C Chen, S Zhu, Y Wei - IEEE transactions on cybernetics, 2018 - ieeexplore.ieee.org
This paper studies one type of delayed memristor-based fractional-order neural networks
(MFNNs) on the finite-time stability problem. By using the method of iteration, contracting …

[HTML][HTML] Lyapunov stability analysis of fractional nonlinear systems

S Liu, W Jiang, X Li, XF Zhou - Applied Mathematics Letters, 2016 - Elsevier
Lyapunov direct method provides a very effective approach to analyze stability of nonlinear
systems, however, the well-known Leibniz rule is not suitable for fractional derivatives. This …