Abstract
In this paper, by means of Darbo’s fixed point theorem, we establish the existence of solutions to a nonlinear discrete fractional mixed type sum-difference equation boundary value problem in a Banach space. Additionally, as an application, we give an example to demonstrate the main result.
Highlights
Throughout this paper, we denote Na = {a, a +, a +, . . .} and Nba = {a, a +, . . . , b} for a, b ∈ R with b – a ∈ N
In Section, we establish the existence result of problem ( . ), and we present in Section an example illustrating the abstract theory
We show that the operator F : D → D is a strict contraction
Summary
We consider the following discrete fractional mixed type sum-difference equation boundary value problem in Banach space E:. Lv and Feng [ ] initially introduced some basic conceptions and fundamental results on discrete fractional calculus for any Banach-valued function and using of the contraction mapping principle, investigated the existence and uniqueness of solutions for a class of fractional mixed type sum-difference equation boundary value problems on discrete infinite intervals in Banach spaces. It is worth reminding that here we use α, αC, and αX to denote the Kuratowski noncompactness measure of bounded sets in Banach spaces E, C(Nba, E), and X, respectively. If (C ) and (C ) hold, for any > , there exists a positive number N ∈ Nβ– such that (F u)(t ).
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