On two abstract Caputo multi-term sequential fractional boundary value problems under the integral conditions

In this research, we investigate some conditions on the existence of solutions for two abstract multi-term sequential boundary value problems defined with the help of the Caputo derivatives. To do this, we consider some hypotheses on the existing single-valued and multi-valued functions defined in the given fractional differential equation and inclusion. In fact, according to the conditions of two versions of the Krasnoselskii's fixed point theorems, we prove our required criteria which confirm the existence of solutions for the suggested boundary value problems. Finally, we consider some examples to show the consistency of our results numerically.