Research Article Theory of Fractional Hybrid Problems in the Frame of ψ- Hilfer Fractional Operators Saeed M. Ali , 1 Wedad Albalawi , 2 Mohammed S. Abdo , 3 Heba Y. Zahran , 4,5,6 and Abdel-Haleem Abdel-Aty 7,8 1 Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P.O. Box 1982, Dammam 34151, Saudi Arabia 2 Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia 3 Department of Mathematics, Hodeidah University, P.O. Box 3114, Al-Hudaydah, Yemen 4 Laboratory of Nano-Smart Materials for Science and Technology (LNSMST), Department of Physics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia 5 Research Center for Advanced Materials Science (RCAMS), King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia 6 Nanoscience Laboratory for Environmental and Biomedical Applications (NLEBA), Metallurgical Lab. 1, Department of Physics, Faculty of Education, Ain Shams University, Roxy, Cairo 11757, Egypt 7 Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia 8 Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt Correspondence should be addressed to Mohammed S. Abdo; msabdo@hoduniv.net.ye Received 16 December 2021; Revised 15 February 2022; Accepted 17 February 2022; Published 20 March 2022 Academic Editor: Youssri Hassan Youssri Copyright © 2022 Saeed M. Ali et al. This 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. In the present manuscript, we develop and extend a qualitative analysis for two classes of boundary value problems for nonlinear hybrid fractional differential equations with hybrid boundary conditions involving a ψ-Hilfer fractional order derivative introduced by Sousa and de Oliveira (2018). First, we derive the equivalent fractional integral equations to the proposed problems from some properties of the ψ-fractional calculus. Next, we establish the existence theorems in the weighted spaces via equivalent fractional integral equations with the help of Dhage’s fixed-point theorem (2004). Besides, for an adequate choice of the kernel ψ, we recover most of all the preceding results on fractional hybrid equations. Finally, two examples are constructed to make our main findings effective. 1. Introduction Recently, a lot of keen interest in the topic of fractional calcu- lus (FC) has been shown by many researchers and investiga- tors in view of its theoretical development and extensive applications in the applied and natural sciences. Different types of differential and integral operators of arbitrary orders have been introduced by Kilbas et al. [1]. In the same regard, Atangana and Baleanu [2] proposed a new fractional deriva- tive (FD) based on a nonsingular and nonlocal kernel. On the advanced improvement of the FC without a singular kernel of the sinc function, the Yang-Gao-Machado-Baleanu FD was introduced in [3]. Some properties of the FD without a singular kernel were introduced by Lozada and Nieto [4]. Hilfer in [5] proposed a generalization of the Riemann- Liouville fractional derivative (RLFD) and Caputo fractional derivative (CFD) when the author deliberated fractional time evolution in physical phenomena. The author named it a generalized FD, whereas more recently, it was named the Hilfer fractional derivative (HFD). This operator carries two parameters (α, β) that may be decreased to the RLFD and CFD definitions if β =0 and β =1, respectively. So, such Hindawi Journal of Function Spaces Volume 2022, Article ID 1079214, 11 pages https://doi.org/10.1155/2022/1079214