Study on the stability for implicit second-order differential equation via integral boundary conditions

Document Type : Research Article


1 Department of Mathematics, Alexandria University, Alexandria, Egypt

2 Department of Mathematics, College of Science, Qassim University, P.O. Box 6644 Buraidah 51452, Saudi Arabia

3 Department of Mathematics, The International University of Beirut, Beirut, Lebanon


In this paper, the existence and the Ulam-Hyers stability of solutions for the implicit second-order  differential equations are investigated via fractional-orders integral boundary conditions by direct application of the Banach contraction principle.  Finally, we  present some particular cases and two examples to illustrate our results.