Abbas, Syed Existence of solutions to fractional order ordinary and delay differential equations and applications. (English) Zbl 1211.34096 Electron. J. Differ. Equ. 2011, Paper No. 09, 11 p. (2011). Summary: We discuss the existence and uniqueness of solutions to fractional order ordinary and delay differential equations. We apply our results to single species model of Lotka Volterra type. Fixed point theorems are the main tool used here to establish the existence and uniqueness results. First, we use Banach contraction principle and then Krasnosel’skii’s fixed point theorem to show the existence and uniqueness of the solution under certain conditions. Moreover, we prove that the solution can be extended to the maximal interval of existence. Cited in 55 Documents MSC: 34K37 Functional-differential equations with fractional derivatives 34A08 Fractional ordinary differential equations 47N20 Applications of operator theory to differential and integral equations Keywords:fractional differential equation; fixed point theorems; maximum interval of existence PDFBibTeX XMLCite \textit{S. Abbas}, Electron. J. Differ. Equ. 2011, Paper No. 09, 11 p. (2011; Zbl 1211.34096) Full Text: EuDML EMIS