@article{Moumen2023, 
author = {Abdelkader Moumen and Ramsha Shafqat and Zakia Hammouch and Azmat Ullah Khan Niazi and Mdi Begum Jeelani},
title = {Stability results for fractional integral pantograph differential equations involving two Caputo operators},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {6009-6025},
keywords = {existence, fixed point, fractional derivative, Ulam-Hyers stability, fractional pantograph equation},
url = {https://www.sciopen.com/article/10.3934/math.2023303},
doi = {10.3934/math.2023303},
abstract = {In this paper, we investigate the existence-uniqueness, and Ulam Hyers stability (UHS) of solutions to a fractional-order pantograph differential equation (FOPDE) with two Caputo operators. Banach's fixed point (BFP) and Leray-alternative Schauder's are used to prove the existence- uniqueness of solutions. In addition, we discuss and demonstrate various types of Ulam-stability for our problem. Finally, an example is provided for clarity.}
}