University of Guilan Journal of Mathematical Modeling 2345-394X 10 2 2022 06 01 Study on the stability for implicit second-order differential equation via integral boundary conditions 331 348 5231 10.22124/jmm.2021.19931.1725 EN Ahmed Mohamed Ahmed El-Sayed Department of Mathematics, Alexandria University, Alexandria, Egypt Hind Hassan Gaber Hashem Department of Mathematics, College of Science, Qassim University, P.O. Box 6644 Buraidah 51452, Saudi Arabia Shorouk Mahmoud Al-Issa Department of Mathematics, The International University of Beirut, Beirut, Lebanon Journal Article 2021 06 20 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. Caputo fractional derivative second-order fractional-order differential equation Green's function boundary value problems nonlocal boundary conditions https://jmm.guilan.ac.ir/article_5231_103a07a6c5ffdae71942c28dcdb8c475.pdf