Existence and finite-time stability results for impulsive fractional differential equations with maxima

Existence and finite-time stability of solutions for a class of nonlinear fractional differential equations with time-varying delays and non-instantaneous impulses

“…On the other hand, finite-time stability analysis is also one of the most crucial themes for fractional systems, such as [23][24][25][26][27]. In detail, in [23,24], the authors investigated finitetime stability of Caputo delta fractional difference equations, and a finite-time stability criterion was proposed for the addressed equations.…”

“…Li and Wang introduced the concept of a delayed Mittag-Leffler type matrix function, and then they presented the finite-time stability results by virtue of a delayed Mittag-Leffler type matrix in [26]. In [27], the authors firstly established an interesting impulsive Gronwall inequality with maxima involving a Hadamard type singular kernel, which could be applied to making a prior estimation. Secondly, they applied the above inequality and fixed point approach to show two existence results.…”

“…However, when we add non-instantaneous impulsive effects into the fractional systems [24][25][26][27], what can we get? Heavily inspired by the papers mentioned, in this paper, we mainly plan to research the existence and finite-time stability results under noninstantaneous impulsive conditions.…”

New existence results for solutions of BVPs for higher order IFDEs involving Riemann-Liouville type Hadamard fractional derivatives

“…In [22], Zhang and Wang Studied the existence and finite-time stability for the following impulsive fractional differential equation…”

Analysis of nonlinear Hadamard fractional differential equations via properties of Mittag–Leffler functions

“…The continuous time random walk theory is another example of arising of fractional derivatives in description of real physical systems (see [16]). There are several existence and stability results for all kinds of Caputo and Riemann-Liouville type nonlinear FDEs with constant coefficients (see [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]), and Hadamard type nonlinear FDEs without constant coefficient (see [1,Chapter 13] and [37][38][39][40][41][42][43]). However, the development of a related theory for Hadamard type nonlinear FDEs with constant coefficient is still in its infancy.…”