Some Existence Results for High Order Fractional Impulsive Differential Equation on Infinite Interval. (22nd October 2020)

• Record Type: Journal Article
• Authors: Hao, Zhaocai; Wang, Tian
• Other Names: Chen Chuanjun Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-10-22
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/6018273
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : In this paper, we consider the high order impulsive differential equation on infinite interval D 0 + α u t + f t, u t, J 0 + β u t, D 0 + α − 1 u t = 0, t ∈ 0, ∞ ∖ t k k = 1 m △ u t k = I k u t k, t = t k, k = 1, …, m u 0 = u ′ 0 = ⋯ = u n − 2 0 = 0, D 0 + α − 1 u ∞ = u 0 By applying Schauder fixed points and Altman fixed points, we obtain some new results on the existence of solutions. The nonlinear term of the equation contains fractional integral operator J β u t and lower order derivative operator D 0 + α − 1 u t . An example is presented to illustrate our results.