University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Theory of Hybrid Fractional Differential Equations with Complex Order65763496710.22130/scma.2018.72907.295ENDevarajVivekDepartment of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.OmidBaghaniDepartment of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.KuppusamyKanagarajanDepartment of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.Journal Article20171003We develop the theory of hybrid fractional differential equations with the complex order $thetain mathbb{C}$, $theta=m+ialpha$, $0<mleq 1$, $alphain mathbb{R}$, in Caputo sense. Using Dhage's type fixed point theorem for the product of abstract nonlinear operators in Banach algebra; one of the operators is $mathfrak{D}$- Lipschitzian and the other one is completely continuous, we prove the existence of mild solutions of initial value problems for hybrid fractional differential equations. Finally, an application to solve one-variable linear fractional Schr"odinger equation with complex order is given.http://scma.maragheh.ac.ir/article_34967_a19fd276ba6778bbb6bed7f43599acca.pdf