Theory of Hybrid Fractional Differential Equations With Complex Order

We develop the theory of hybrid fractional differentialequations with the complex order θ ∈ c, θ = m + iα, 0 < m ≤ 1, α ∈ 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 d- lipschitzian and the other one is com-pletely 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 schrodinger equation with complex order is given.