@article{Al Elaiw2023, 
author = {Abeer Al Elaiw and Farva Hafeez and Mdi Begum Jeelani and Muath Awadalla and Kinda Abuasbeh},
title = {Existence and uniqueness results for mixed derivative involving fractional operators},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {3},
pages = {7377-7393},
keywords = {fractional derivatives, integro-differential equations, pantograph equations, existence conditions},
url = {https://www.sciopen.com/article/10.3934/math.2023371},
doi = {10.3934/math.2023371},
abstract = {In this article, we discuss the existence and uniqueness results for mix derivative involving fractional operators of order    β  ∈  (  1  ,  2  ) and    γ  ∈  (  0  ,  1  ). We prove some important results by using integro-differential equation of pantograph type. We establish the existence and uniqueness of the solutions using fixed point theorem. Furthermore, one application is likewise given to represent our fundamental results.}
}