Existence of solutions to boundary value problem of fractional differential equations with impulsive

• Main Authors: Weihua JIANG, Qingmin LI, Cailian ZHOU
• Format: Article
• Language: zho
• Published: Hebei University of Science and Technology 2016-12-01
• Series: Journal of Hebei University of Science and Technology
• Subjects: analytic theory of ordinary differential equation; impulse; contraction mapping theorem; Krasnoselskii’s fixed point theorem; boundary value problem; the half line
• Online Access: http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201606007&flag=1&journal_

In order to solve the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line, the existence of solutions to the boundary problem is specifically studied. By defining suitable Banach spaces, norms and operators, using the properties of fractional calculus and applying the contraction mapping principle and Krasnoselskii's fixed point theorem, the existence of solutions for the boundary value problem of fractional impulsive differential equations with countable impulses and integral boundary conditions on the half line is proved, and examples are given to illustrate the existence of solutions to this kind of equation boundary value problems.