Gayathri, B.; Murugesu, R.; Rajasingh, J. Existence of solutions of some impulsive fractional integrodifferential equations. (English) Zbl 1252.45004 Int. J. Math. Anal., Ruse 6, No. 17-20, 825-836 (2012). This paper deals with the existence of solutions of some impulsive fractional integrodifferential equations with finite number of impulses: \[ D^{\alpha}u(t) = f(t, u(t), \int_{t_0}^t a(t -s)g(t, u(t))dt);\quad t \in [t_0, a],\;t \neq t_k,\;k = 1, \dots, m, \] with the initial condition \[ D^{\alpha-1}u(t_0) = u_0;\quad (t - t_0)^{1-\alpha}u(t)|_{t=t_0} = \frac{u_0}{\Gamma(\alpha)}, \] and subject to the impulsive conditions \[ D^{\alpha-1}(u(t_k^+) - u(t_k^-)) = I_k(t);\quad t = t_k,\;k = 1, 2, \dots, m; \]\[ (t - t_k)^{1-\alpha}u(t^+)|_{t=t_k} = \frac{I_k(t_k)}{\Gamma(\alpha)},\quad k = 1, \dots \] The existence and uniqueness of local solutions and global solutions are established via the Schauder’s fixed point theorem and the Brouwer’s fixed point theorem, respectively. Reviewer: Iulian Stoleriu (Iaşi) Cited in 4 Documents MSC: 45J05 Integro-ordinary differential equations 45G10 Other nonlinear integral equations 26A33 Fractional derivatives and integrals Keywords:Schauder’s fixed point theorem; Brouwer’s fixed point theorem; Caputo fractional derivative; impulsive fractional integrodifferential equations; local solutions; global solutions PDFBibTeX XMLCite \textit{B. Gayathri} et al., Int. J. Math. Anal., Ruse 6, No. 17--20, 825--836 (2012; Zbl 1252.45004) Full Text: Link