Research Article On Atangana–Baleanu-Type Nonlocal Boundary Fractional Differential Equations Mohammed A. Almalahi , 1 Satish K. Panchal, 2 Mohammed S. Abdo , 3 and Fahd Jarad 4,5 1 Department of Mathematics, Hajjah University, Hajjah, Yemen 2 Department of Mathematics, Dr.Babasaheb Ambedkar Marathwada University, Aurangabad, Maharashtra 431001, India 3 Department of Mathematics, Hodeidah University, Al-Hudaydah, Yemen 4 Department of Mathematics, Çankaya University, 06790 Etimesgut, Ankara, Turkey 5 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan Correspondence should be addressed to Mohammed A. Almalahi; dralmalahi@gmail.com and Fahd Jarad; fahd@cankaya.edu.tr Received 18 December 2021; Accepted 26 January 2022; Published 18 March 2022 Academic Editor: Shrideh K. Q. Al-Omari Copyright © 2022 Mohammed A. Almalahi et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is research paper is devoted to investigating two classes of boundary value problems for nonlinear Atangana–Baleanu-type fractional differential equations with Atangana–Baleanu fractional integral conditions. e applied fractional derivatives work as the nonlocal and nonsingular kernel. Upon using Krasnoselskii’s and Banach’s fixed point techniques, we establish the existence and uniqueness of solutions for proposed problems. Moreover, the Ulam–Hyers stability theory is constructed by using nonlinear analysis. Eventually, we provide two interesting examples to illustrate the effectiveness of our acquired results. 1. Introduction Fractional calculus and its potential applications have be- come a powerful tool to model many complex phenomena in apparently wide-ranging fields of science and technology [1–8]. To meet the needs of modeling many practical problems in different fields of science and engineering, some researchers have realized the necessity development of the concept of fractional calculus by searching for new fractional derivatives with different singular or nonsingular kernels. From this perspective, new fractional operators have turned into the best effective tool of numerous specialists and re- searchers with their contribution to physical phenomena and their performance in applying to real-world problems. Until 2015, all fractional derivatives had only singular kernels. erefore, it is difficult to use these singularities to simulate physical phenomena. In 2015, Caputo and Fabrizio [9] studied a new kind of FD in the exponential kernel. Some propertiesofthisnewtypehadbeendiscussedbyLosadaand Nieto in [10]. A new type and interesting FD with Mittag-Leffler kernels has been investigated by Atangana and Baleanu (A-B) in [11]. Abdeljawad in [12] extended the kind investigated by A-B from order between zero and one to higher arbitrary order and formulated their associated integral operators. Also, he proved some properties such as the existence and uniqueness theorems for two classes of fractional derivative, Riemann type (ABR) and Caputo type (ABC), for initial value problems in higher arbitrary order and proved a Lyapunov-type inequality in the frame of Mittag-Leffler kernels for the ABR fractional boundary value problems of order 2 < α ≤ 3. Abdeljawad and Baleanu, in [13, 14], deliberated the discrete versions of those new operators. For some theoretical works on Atangana–Baleanu FDEs, we refer the reader to a series of papers [15–17]. For important applications and mathematical modeling of the ABC fractional operator, see [18–21]. On the contrary, there are some important numerical approaches regarding non- singular kernels; for example, in [22], via a spectral collo- cation method based on the shifted Legendre polynomials with extending the unknown functions and their derivatives Hindawi Journal of Function Spaces Volume 2022, Article ID 1812445, 17 pages https://doi.org/10.1155/2022/1812445