SOLVABILITY OF NONLINEAR FRACTIONAL LANE-EMDEN-TYPE DELAY EQUATIONS WITH TIME-SINGULAR COEFFICIENTS

We focus on the nonlinear Lane-Emden-type delay problems connected with g-Caputo fractional derivatives. Here, we investigate the problems under the assumption that the source functions have time-singular coefficients. Via the Bielecki-type norm, we derive the existence and uniqueness of mild solutions for the problem. In a special case, by subdividing the interval of time, we obtain a unique mild solution for the problem under a weaker condition than the previous one. Besides, we propose and discuss a new Ulam-Hyers-type stability for the main equation. Meanwhile, a new inequality is established to prove the main results of the paper. Some examples are provided to illustrate the theoretical results.