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Differ Equ Dyn SystDOI 10.1007/s12591-015-0270-xORIGINAL RESEARCHExistence of Solutions for a Coupled FractionalDifferential Equations with Inf i nitely Many PointsBoundary Conditions at Resonance on an UnboundedDomainFu-Dong Ge 1 · Hua-Cheng Zhou 2 · Chun-Hai Kou 3© Foundation for Scientif i c Research and Technological Innovation 2015Abstract Thispaperinvestigatestheexistenceofsolutionsforinf i nitelymanypointsbound-aryvalueproblemsatresonancewithdimker L = 2regardingfractionaldifferentialequationson an unbounded domain. By the well-known coincidence degree theory of Mawhin, it isshown that the considered system under certainly conditions admits at least one solution. Anexample to illustrate the applicability of the given conditions is also given.Keywords Fractional differential equations · Inf i nitely many points · Resonance ·Coincidence degree theory · Unbounded domainMathematics Subject Classif i cation 34A08 · 34B10 · 34B40IntroductionSpurred by the extensive applicability of fractional differential equations in science andengineering, the subject of fractional calculus has attracted increasing attention in the pastthree decades [3,9,12,13,15]. It is worth remarking that initial value problems or boundaryvalue problems for fractional differential equations have been given considerable attentionby many authors, see [6–8,10,20,23] and the references therein. Recently, the existence ofsolutions of the boundary value problems for fractional differential equations at resonancewith dimker L = 1 on f i nite interval have been investigated, see [6–8,20]. More recently,in [5,21], the authors presented the existence of solutions to a coupled system of fractionaldifferential equations at resonance with dimker L = 2 but on f i nite interval. In our previouswork[22],weinvestigatedtheexistenceofsolutionsformulti-pointboundaryvalueproblemsB Hua-Cheng Zhouhczhou@amss.ac.cn1College of Information Science and Technology, Donghua University, Shanghai 201620, China2Academy of Mathematics and Systems Science, Academia Sinica, Beijing 100190, China3Department of Applied Mathematics, Donghua University, Shanghai 201620, China123