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In this paper, we study the nonlocal Cauchy problems of fractional evolution equations with Riemann-Liouville derivative by considering an integral equation which is given in terms of probability density. By using the theory of Hausdorff measure of noncompactness, we establish various existence theorems of mild solutions for the Cauchy problems in the cases C 0 semigroup is compact or noncompact. 2010 AMS Mathematics subject classification. Primary 26A33, 34A08, 35R11. Keywords and phrases. Fractional evolution equations, integral equations, Riemann-Liouville derivative, mild solutions, C 0 semigroup, measure of noncompactness.

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Directed differentiation methods allow acquisition of high-purity cardiomyocytes differentiated from human induced pluripotent stem cells (hiPSCs); however, their immaturity characteristic limits their application for drug screening and regenerative therapy. The rapid electrical pacing of cardiomyocytes has been used for efficiently promoting the maturation of cardiomyocytes, here we describe a simple device in modified culture plate on which hiPSCderived cardiomyocytes can form three-dimensional self-organized tissue rings (SOTRs). Using calcium imaging, we show that within the ring, reentrant waves (ReWs) of action potential spontaneously originated and ran robustly at a frequency up to 4 Hz. After 2 weeks, SOTRs with ReWs show higher maturation including structural organization, increased cardiac-specific gene expression, enhanced Ca 2+-handling properties, an increased oxygenconsumption rate, and enhanced contractile force. We subsequently use a mathematical model to interpret the origination, propagation, and long-term behavior of the ReWs within the SOTRs.