Initial Value Problems of Fractional Order with Fractional Impulsive Conditions

Existence results for multi-term time-fractional impulsive differential equations with fractional order boundary conditions

“…The differential system (1.1) − (1.5) describes diffusion wave character of a phenomena [32,36]. Moreover, instantaneous forces present in the phenomena at certain points may be characterized more precisely by fractional order impulsive conditions (1.3) rather than integer one (see [19,25]). The results are illustrated with a well-analyzed example in Section 4.…”

“…The system (1.1) − (1.3) with boundary conditions (1.4) and (1.5) is a strong motivation of the applications of physical models with papers [19,25,27,28]. Kosmatov [25], Vidushi and Dabas [19] considered the following impulsive model…”

Optimal controls for a class of impulsive fractional differential equations with nonlocal conditions

“…A number of papers extensively study impulsive differential equations with nonlocal differential equations or impulsive conditions only containing integer order derivatives [23,24]. Kosmatov in [25] considered the nonlinear differential equation initial value problem:…”

Existence Results for Fractional Integro-Differential Equations with Fractional Order Non-instantaneous Impulsive Conditions

“…al [13] treated abstract differential equations with fractional derivatives in time t, based on the well developed theory of resolvent operators for integral equations [28]. In [17] N Kosmatov studied the initial value problems of fractional order with fractional impulsive conditions. From the result in [17] and the application of fractional derivative we came to know that the fractional order non-instantaneous impulsive systems were more powerful than those with the integer order impulsive conditions.…”

“…In [17] N Kosmatov studied the initial value problems of fractional order with fractional impulsive conditions. From the result in [17] and the application of fractional derivative we came to know that the fractional order non-instantaneous impulsive systems were more powerful than those with the integer order impulsive conditions.…”