Random Noninstantaneous Impulsive Models for Studying Periodic Evolution Processes in Pharmacotherapy

p-Moment exponential stability of Caputo fractional differential equations with noninstantaneous random impulses

“…FrDEs with instantaneously acting impulses at random times are studied in some papers [10] but there are some inaccuracies in the mixing properties of deterministic variables and random variables, and inaccuracies in the convergence of a sequence of real numbers to a random variable. A similar comment applies in some papers on random impulses in impulsive differential equations [9,46]. In this paper we study nonlinear FrDEs subject to impulses starting abruptly at some random points and their action continue on intervals with a given finite length.…”

Boundedness, periodicity, and conditional stability of noninstantaneous impulsive evolution equations

“…We emphasize that the current approach and proofs are different from Wang et al 23 In particular, we do not need the compactness on either the strongly continuous semigroup or evolution family and remove the contraction conditions in Fečkan et al, 22 Theorem 2.5, Wang et al, 23 Theorem 4 and Muslim et al 24 Theorem 3.7 Of course, we can develop the method in Chen et al 13,32 to study the current results.…”

“…1 Existence and stability results for this new type of impulsive equations have been reported in previous works. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] Periodic solutions of noninstantaneous impulsive equations were studied in previous literature, [22][23][24] and existence results were established by constructing a suitable composite Poincaré operator through some compact embeddings. [25][26][27] A strong contraction condition appeared in the main theorems; see Fečkan et al, 22, Theorem 2.5, Wang et al, 23, Theorem 4 and Muslim et al 24, Theorem 3.7.…”

“…Motivated by Wang et al 23 and Huy and Dang, 30 we extend the study to a nonhomogeneous noninstantaneous impulsive linear evolution equation of the type: and semilinear evolution equation…”

Stability and solvability for a class of optimal control problems described by non-instantaneous impulsive differential equations

“…Now, a large number of references deal with the impulsive differential equations. By the type of impulse, they include the non-instantaneous case [1][2][3][4][5][6][7][8][9][10][11][12] and the instantaneous case [13][14][15][16][17][18][19][20][21][22].…”