Comments on the concept of existence of solution for impulsive fractional differential equations

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

“…There are two viewpoints: (V1): using the classical Caputo derivative and working in each subinterval, determined by the impulses (see, for example, [1,8,13,45]). This approach is based on the idea that on each interval between two consecutive impulses the solution is determined by the differential equation of fractional order.…”

Existence results for an impulsive fractional integro-differential equation with state-dependent delay

“…In latest years, as the historical specialized mathematicians predicted, fractional differential equations have been discovered to be a highly effective tool in many areas, such as viscoelasticity, electro-chemistry, control, porous media, and electromagnetic. For fundamental certainties about fractional systems, one can make reference to the books [20][21][22][23][24], and the papers [25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41], and the references cited therein. Fractional equation with delay features happen in several areas such as medical and physical with statedependent delay or non-constant delay.…”

Existence of solutions to boundary value problem for impulsive fractional differential equations

“…Another concept on solutions of fractional differential equations is presented in [26]. Under assumption (H1) the functional ϕ : E α → R is continuous, differentiable and for…”