Functional impulsive differential equation of order α∈(1,2) with nonlocal initial and integral boundary conditions

Abstract

The main work is related to show the existence and uniqueness of solution for the fractional impulsive differential equation of order α∈(1,2) with an integral boundary condition and finite delay. Using the application of the Banach and Sadovaskii fixed‐point theorems, we obtain the main results. An example is presented at the end to verify the results of the paper. Copyright © 2016 John Wiley & Sons, Ltd.

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…”

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