TY - JOUR AU - Carvalho, Alexandre Nolasco AU - Carvalho-Neto, Paulo M. Carvalho-Neto AU - MarĂ­n-Rubio, Pedro AU - Andrade, Bruno de PY - 2015/06/01 Y2 - 2024/03/28 TI - Semilinear fractional differential equations: global solutions, critical nonlinearities and comparison results JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 45 IS - 2 SE - DO - 10.12775/TMNA.2015.022 UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2015.022 SP - 439 - 467 AB - In this work we study several questions concerning to abstract fractional Cauchy problems of order $\alpha\in(0,1)$. Concretely, we analyze the existence of local mild solutions for the problem, and its possible continuation to a maximal interval of existence. The case of critical nonlinearities and corresponding regular mild solutions is also studied. Finally, by establishing some general comparison results, we apply them to conclude the global well-posedness of a fractional partial differential equation coming from heat conduction theory. ER -