Abstract
In this paper, by using the Banach contraction principle and the Schauder’s fixed point theorem, we investigate existence results for a fractional impulsive sum-difference equations with periodic boundary conditions. Moreover, we also establish different kinds of Ulam stability for this problem. An example is also constructed to demonstrate the importance of these results.
Highlights
We study the following periodic boundary value problem for fractional impulsive difference-sum equations: h i α u(t) = F t + α − 1, u(t + α − 1), Ψγ u(t + α − 1), t ∈ N0,T, t + α − 1 6= tk
By using the Banach contraction principle and the Schauder’s fixed point theorem, we aim to prove the existence results for the problem (1) and (2)
(t − s + α − 2)α−1 F s, u(s), Ψγ u(s), t ∈ Nt0,t1
Summary
We study the following periodic boundary value problem for fractional impulsive difference-sum equations:. Some interesting results on fractional difference calculus have been studied, which has helped to develop the basic theory of this calculus; see [10–40] and references cited therein. The studies of boundary value problems for fractional difference equations are shown both extensive and more complex of conditions. There are some recent papers to study the existence and stability results of fractional difference equation [44–51]. A few paper has been made to develop the theory of the existence and stability results of fractional difference equations with impulse [52,53]. These results are the motivation for this research.
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