Agarwal, Ravi P.; Ahmad, Bashir Existence of solutions for impulsive anti-periodic boundary value problems of fractional semilinear evolution equations. (English) Zbl 1226.26005 Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 18, No. 4, 457-470 (2011). Summary: We study the existence and uniqueness of solutions for impulsive semilinear evolution equations of fractional order \(q\in(1,2]\) with anti-periodic boundary conditions. The contraction mapping principle and Krasnosel’skii’s fixed point theorem are applied to prove the main results. An illustrative example is also presented. Cited in 26 Documents MSC: 26A33 Fractional derivatives and integrals 34A34 Nonlinear ordinary differential equations and systems 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:evolution equations of fractional order; impulse; anti-periodic boundary conditions; existence; contraction mapping principle; Krasnoselskii’s fixed point theorem PDFBibTeX XMLCite \textit{R. P. Agarwal} and \textit{B. Ahmad}, Dyn. Contin. Discrete Impuls. Syst., Ser. A, Math. Anal. 18, No. 4, 457--470 (2011; Zbl 1226.26005) Full Text: Link