Two fractional hybrid and non-hybrid boundary value problems

In the current research, we derive some existence and stability criteria for two hybrid and non-hybrid differential equations of fractional order. By utilizing an analytical technique based on the generalized Dhage's fixed point result, we verify desired existence theorem for the hybrid problem. Also, we consider a special case as a non-hybrid problem and by using the Kuratowski's measure of non-compactness, we establish a new existence criterion. Eventually, we turn to investigation of the stability of solutions for the non-hybrid problem by applying the generalized Gronwall's inequality. Finally, we provide an example to illustrate the relevant non-hybrid result.