Existence and uniqueness of mild and classical solutions to fractional order Hadamard-type Cauchy problem


Qutaibeh Katatbeh - Department of Mathematics and Statistics, Faculty of Science and Arts, Jordan University of Science and Technology, Irbid 22110, Jordan. Ahmad Al-Omari - Faculty of Sciences, Department of Mathematics, Al al-Bayt University, P. O. Box 130095, Mafraq 25113, Jordan.


We consider the existence and uniqueness of a mild and classical solution to impulsive nonlocal conditions fractional-order Hadamard-type Cauchy problem. The results are obtained by means of fixed point methods. Finally, we illustrate our results by an example of fractional-order Hadamard-type Cauchy problem.