Positive solutions to fractional differential equations involving Stieltjes integral conditions

In this paper, we investigate nonlocal boundary value problems for fractional differential equations with dependence on the first-order derivatives and deviating arguments. Sufficient conditions which guarantee the existence of at least three positive solutions are new and obtained by using the Avery–Peterson theorem. We discuss problems (1) and (2) when argument ββ can change the character on [0, 1], so in some subinterval I of [0, 1], it can be delayed in I   and advanced in [0,1]⧹I[0,1]⧹I. Moreover in our discussion problem (2) depends on delayed argument αα. Examples illustrate the results.