Existence of solutions of impulsive boundary value problems for singular fractional differential systems

• Main Author: Yuji Liu
• Format: Article
• Language: English
• Published: Institute of Mathematics of the Czech Academy of Science 2017-12-01
• Series: Mathematica Bohemica
• Subjects: singular fractional differential system; impulsive boundary value problem; fixed point theorem
• Online Access: http://mb.math.cas.cz/full/142/4/mb142_4_6.pdf

A class of impulsive boundary value problems of fractional differential systems is studied. Banach spaces are constructed and nonlinear operators defined on these Banach spaces. Sufficient conditions are given for the existence of solutions of this class of impulsive boundary value problems for singular fractional differential systems in which odd homeomorphism operators (Definition 2.6) are involved. Main results are Theorem 4.1 and Corollary 4.2. The analysis relies on a well known fixed point theorem: Leray-Schauder Nonlinear Alternative (Lemma 2.1). An example is given to illustrate the efficiency of the main theorems, see Example 5.1.