University of MaraghehSahand Communications in Mathematical Analysis2322-580715120190701Theory of Hybrid Fractional Differential Equations with Complex Order65763496710.22130/scma.2018.72907.295ENDevaraj VivekDepartment of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.Omid BaghaniDepartment of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O. Box 397, Sabzevar, Iran.Kuppusamy KanagarajanDepartment 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