Abstract
In this paper, we study the existence and uniqueness of solutions for two classes of boundary value problems for impulsive Caputo type fractional Hahn difference equations, by using the Banach contraction mapping principle and the nonlinear alternative of Leray–Schauder. The obtained results are well illustrated by examples.
Highlights
Introduction and preliminariesOur purpose of this paper is to establish the existence and uniqueness results for two impulsive fractional Hanh difference boundary value problems
We investigate the impulsive Hahn difference boundary value problem (1)
We find that θk = (1/2) + k ∈ Jk, k = 0, 1, 2, 3
Summary
We define intervals Jk = [tk, tk+1), k = 0, 1, 2, . We define the space PC(J, R) = {x : J → R : x(t) is continuous everywhere except for some tk at which x(tk+) and x(tk–) exist and x(tk+) = x(tk), k = 1, 2, . 1, we replace all parameters, a, q, ω and ν of fractional quantum Hahn calculus in Definitions 3–5 by tk, qk, ωk and νk, k = 0, 1, 2, . The fractional quantum Hahn calculus is used to establish the existence and uniqueness results for the impulsive fractional Hahn difference boundary value problems (1) and (2)
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